Adaptive Neural Networks Finite-Time Optimal Control for a Class of Nonlinear Systems

Distributed observer-based prescribed-time affine formation control for underactuated unmanned surface vessels under DoS attack

This study addresses the control challenges of distributed prescribed-time maneuvers for underactuated unmanned surface vessels (USVs) operating in affine formation under adverse conditions, including ocean disturbances, unmodeled dynamics, and denial-of-service (DoS) attacks. The research develops a control scheme that enables USVs to perform complex maneuvers such as translation, shearing, rotation, and scaling, despite intermittent communication failures due to periodic DoS attacks. The approach integrates a distributed prescribed-time observer (DPTO) for each vessel to monitor local time-varying desired states, coupled with an adaptive prescribed-time local tracking control (APTLTC) strategy that drives the USV to track the desired states. The effectiveness and robustness of this control solution are validated through theoretical analysis and simulation, demonstrating significant resilience against network disruptions. This study contributes to safer maritime operations by providing a robust control framework for underactuated USVs under cyber-physical threats.

Finite-Time Adaptive Dynamic Programming for Affine-Form Nonlinear Systems

Inspired by the fusion of state optimization and finite-time convergence, the finite-time optimal control (FTOC) for the affine-form nonlinear systems is investigated in this article. To achieve optimal stability with finite response time, a novel finite-time adaptive dynamic programming (FTADP) is presented for the affine-form nonlinear systems. By mapping the value function into finite-time stability space with the transformation function, the Bellman equation with finite-time stability space is first obtained. Then, by solving the Hamilton-Jacobi-Bellman (HJB) equation, the new FTOC strategy is presented with the theoretical finite-time stability description. Furthermore, to solve the above optimal controller with nonlinearity characteristic, the novel adaptive dynamic programming (ADP) based on the finite-time critic-actor offline neural network (NN) approximation algorithm is implemented, and the corresponding finite-time convergence characteristic is illustrated theoretically. Eventually, the application analysis on the circuit systems shows that the proposed FTADP has superiority compared with general optimal control.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Adaptive fuzzy tracking control for a class of time-varying output constrained nonlinear systems with non-affine nonlinear faults

This paper investigates a tracking control issue for a class of time-varying output constrained nonlinear systems subject to non-affine nonlinear faults and virtual control coefficients. In the controller design process, the nonlinear function is approximated by fuzzy logic systems. Utilizing a feasible function to convert the system, a new transformation strategy is proposed to handle the system with time-varying output constraints or without output constraints. The mean value theorem is applied to split non-affine faults, and the Nussbaum-type function is used to eliminate the effect of the unknown directional affine variable gain of input resulted from non-affine faults. Combined with adaptive fuzzy backstepping technology and the error transformation function, a new control strategy is presented, which not only deals with the time-varying output constraint but also handles non-affine faults, effectively. Finally, all closed-loop system signals are bounded, and the tracking error can converge to a small preset set. Two simulations are performed to confirm the validity of the presented strategy.

Disturbance Observer-Based Adaptive Intelligent Control of Marine Vessel With Position and Heading Constraint Condition Related to Desired Output

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

Nearly Optimal Control for Mixed Zero-Sum Game Based on Off-Policy Integral Reinforcement Learning

In this article, we solve a class of mixed zero-sum game with unknown dynamic information of nonlinear system. A policy iterative algorithm that adopts integral reinforcement learning (IRL), which does not depend on system information, is proposed to obtain the optimal control of competitor and collaborators. An adaptive update law that combines critic-actor structure with experience replay is proposed. The actor function not only approximates optimal control of every player but also estimates auxiliary control, which does not participate in the actual control process and only exists in theory. The parameters of the actor-critic structure are simultaneously updated. Then, it is proven that the parameter errors of the polynomial approximation are uniformly ultimately bounded. Finally, the effectiveness of the proposed algorithm is verified by two given simulations.

Self-Constructing Fuzzy Neural Fractional-Order Sliding Mode Control of Active Power Filter

In this article, a fractional-order sliding mode control (FOSMC) scheme is proposed for mitigating harmonic distortions in the power system, whereby a self-constructing recurrent fuzzy neural network (SCRFNN) is used to weaken the effect of compound nonlinearity caused by unknown uncertainties and environmental fluctuations. The fractional-order sliding mode controller (SMC) is constructed to maintain the control system to be asymptotically stable and a fractional-order calculus is introduced into an SMC to soften the sliding manifold design and realize chattering reduction. Considering parameter variations existing in the power system model, SCRFNN is adopted to approximate the unknown dynamics, which is able to dynamically update network structure by optimizing the fuzzy division, and a feedback connection is incorporated into the feedforward neural network, which is regarded as a storage unit to enhance the capability of coping with temporal problem. The control scheme combining the FOSMC with the SCRFNN can make the tracking error and its time derivative converge to zero. Experimental studies demonstrate the validity of the designed scheme, and comprehensive comparisons illustrate its superiority in harmonic suppression and high robustness.

Disturbance Observer-Based Adaptive Neural Network Output Feedback Control for Uncertain Nonlinear Systems

This article is devoted to the output feedback control of nonlinear system subject to unknown control directions, unknown Bouc-Wen hysteresis and unknown disturbances. During the control design process, the design obstacles caused by unknown control directions and Bouc-Wen hysteresis are eliminated by introducing linear state transformation and a new coordinate transformation, which avoids using the Nussbaum function with high-frequency oscillation to deal with the issue. Besides, to settle the issue caused by the unknown disturbances, a novel nonlinear disturbance observer is designed, which has the characteristics of simple structure, low coupling, and easy implementation. Especially, a compensation item is constructed to offset the redundant items generated in the backstepping design process. Simultaneously, using the neural network and backstepping technology, an output feedback controller is devised. The controller ensures that all closed-loop signals are bounded, and the system output, state observation error, and disturbance observation error converge to a small neighborhood of the origin. Finally, to illustrate the effectiveness of the proposed scheme, simulation verification is carried out based on a numerical example and a Nomoto ship model.

Nonsingular Practical Fixed-Time Adaptive Output Feedback Control of MIMO Nonlinear Systems

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

Data-Driven Policy Iteration for Nonlinear Optimal Control Problems

The design of optimal control laws for nonlinear systems is tackled without knowledge of the underlying plant and of a functional description of the cost function. The proposed data-driven method is based only on real-time measurements of the state of the plant and of the (instantaneous) value of the reward signal and relies on a combination of ideas borrowed from the theories of optimal and adaptive control problems. As a result, the architecture implements a policy iteration strategy in which, hinging on the use of neural networks, the policy evaluation step and the computation of the relevant information instrumental for the policy improvement step are performed in a purely continuous-time fashion. Furthermore, the desirable features of the design method, including convergence rate and robustness properties, are discussed. Finally, the theory is validated via two benchmark numerical simulations.

Real-Time Leak Location of Long-Distance Pipeline Using Adaptive Dynamic Programming

In traditional leak location methods, the position of the leak point is located through the time difference of pressure change points of both ends of the pipeline. The inaccurate estimation of pressure change points leads to the wrong leak location result. To address it, adaptive dynamic programming is proposed to solve the pipeline leak location problem in this article. First, a pipeline model is proposed to describe the pressure change along pipeline, which is utilized to reflect the iterative situation of the logarithmic form of pressure change. Then, under the Bellman optimality principle, a value iteration (VI) scheme is proposed to provide the optimal sequence of the nominal parameter and obtain the pipeline leak point. Furthermore, neural networks are built as the VI scheme structure to ensure the iterative performance of the proposed method. By transforming into the dynamic optimization problem, the proposed method adopts the estimation of the logarithmic form of pressure changes of both ends of the pipeline to locate the leak point, which avoids the wrong results caused by unclear pressure change points. Thus, it could be applied for real-time leak location of long-distance pipeline. Finally, the experiment cases are given to illustrate the effectiveness of the proposed method.

Novel Adaptive Event-Triggered Fuzzy Command Filter Control for Slowly Switched Nonlinear Systems With Constraints

This article addresses the adaptive fuzzy control problem for switched nonlinear systems with state constraints. The unified barrier function (UBF) is introduced to solve the time-varying state constraints, which removes the feasibility conditions. By integrating command filter into backstepping control to avoid the "explosion of complexity." In addition, a novel event-triggered strategy is designed to deal with the asynchronous switching between subsystems and controllers without limiting the maximum asynchronous time, and mitigate the communication burden. Also, a new threshold function is introduced to overcome the difficulty of discontinuous triggering error at the switching instants. Then, by combining the improved admissible edge-dependent average dwell-time (AED-ADT) method with Lyapunov stability analysis, it is proved that all system signals are bounded and do not violate the predefined constraints under given switching rule. Finally, the numerical simulation results verify the superiority of the proposed algorithm, and the algorithm is applied to a ship maneuvering system.

Fast Finite-Time Control for Nonaffine Stochastic Nonlinear Systems Against Multiple Actuator Constraints via Output Feedback

This research addresses the finite-time control problem for nonaffine stochastic nonlinear systems with actuator faults and input saturation. Specifically, a new finite-time control scheme is constructed based on the adaptive backstepping framework, with the usage of a state observer and taking advantage of the universal approximation capability of the fuzzy-logic system (FLS). The novelty of this work is that it considers the output feedback problem of a completely nonaffine stochastic system and incorporates the idea of the dynamic surface control (DSC) design. By using the Lyapunov stability theory, all the signals of the controlled system can be semiglobal finite-time stable in probability (SGFSP) while the system is imposed with multiple actuator constraints. In the meantime, the problem of "complexity explosion" is avoided. Two simulation examples are given to demonstrate the validity of the presented strategy.

Enhanced Fuzzy Fault Estimation of Discrete-Time Nonlinear Systems via a New Real-Time Gain-Scheduling Mechanism

The problem of enhancing the robust performance of nonlinear fault estimation (FE) is addressed by proposing a novel real-time gain-scheduling mechanism for discrete-time Takagi-Sugeno fuzzy systems. The real-time status of the operating point for the considered nonlinear plant is characterized by using these available normalized fuzzy weighting functions at both the current and the past instants of time. To achieve this, the developed fuzzy real-time gain-scheduling mechanism produces different switching modes by introducing key tunable parameters. Thus, a pair of exclusive FE gain matrices is designed for each switching mode on the strength of time-varying balanced matrices developed in this study, respectively. Since the implementation of more FE gain matrices can be scheduled according to the real-time status of the operating point at each sampling instant, the robust performance of nonlinear FE will be enhanced over the previous methods to a great extent. Finally, considerable numerical comparisons are implemented in order to illustrate that the proposed method is much superior to those existing ones reported in the literature.

A Sensor-Aided System for Physical Perfect Control Applications in the Continuous-Time Domain

The recently introduced continuous-time perfect control algorithm has revealed a great potential in terms of the maximum-speed and maximum-accuracy behaviors. However, the discussed inverse model-originated control strategy is associated with considerable energy consumption, which has exceeded a technological limitation in a number of industrial cases. In order to prevent such an important drawback, several solutions could be considered. Therefore, an innovative perfect control scheme devoted to the multivariable real-life objects is investigated in this paper. Henceforth, the new IMC-related approach, strongly supported by the vital sensor-aided system, can successfully be employed in every real-time engineering task, where the precision of conducted processes plays an important role. Theoretical and practical examples strictly confirm the big implementation potential of the new established method over existing ones. It has been seen that the new perfect control algorithm outperforms the classical control law in the form of LQR (considered in two separate ways), which is clearly manifested by almost all simulation examples. For instance, in the case of the multi-tank system, the performance indices ISE, RT, and MOE for LQR without an integration action have been equal to 2.431, 2.4×102, and 3.655×10-6, respectively, whilst the respective values 1.638, 1.58×102, and 1.514×10-7 have been received for the proposed approach.

Adaptive Event-Triggered Neural Network Control for Switching Nonlinear Systems With Time Delays

The adaptive event-triggered-based neural network control is explored for switching nonlinear systems with nonstrict-feedback structure and time-varying delays in this article. First, the switching observer is designed to estimate the unmeasurable states. Due to the existence of time-varying input delay, a compensation system is introduced. The average dwell-time (ADT) scheme and the event-triggered controller are established. Furthermore, the semiglobal uniform ultimate boundedness (SGUUB) of all the variables in the closed-loop system is achieved and the Zeno behavior is avoided. Finally, the numerical simulation shows that our proposed control approach is effective.

Prescribed performance adaptive event-triggered consensus control for multiagent systems with input saturation

In this paper, a prescribed performance adaptive event-triggered consensus control method is developed for a class of multiagent systems with the consideration of input dead zone and saturation. In practical engineering applications, systems are inevitably suffered from input saturation. In addition, input dead zone is widely existing. As the larger signal is limited and the smaller signal is difficult to effectively operate, system efficacious input encounters unknown magnitude limitations, which seriously impact system control performance and even lead to system instability. Furthermore, when constrained multiagent systems are required to converge quickly, the followers would achieve it with drastic and quick variation of states, which may violate the constraints and even cause security problems. To address those problems, an adaptive event-triggered consensus control is proposed. By constructing the transform function and the barrier Lyapunov function, while state constrained is guaranteed, multiagent systems quickly converge with prescribed performance. Finally, some examples are adopted to confirm the effectiveness of the proposed control method.

Adaptive Fuzzy Finite-Time Fault-Tolerant Consensus Tracking Control for High-Order Multiagent Systems With Directed Graphs

This article investigates the distributed adaptive fuzzy finite-time fault-tolerant consensus tracking control for a class of unknown nonlinear high-order multiagent systems (MASs) with actuator faults and high powers (ratio of positive odd rational numbers). The fault models include both loss of effectiveness and bias fault. Compared with existing similar results, the MASs considered here are more general and complex, which include the special case when the powers are equal to 1. Besides, the functions in this article are completely unknown and do not need to satisfy any growth conditions. In the backstepping framework, an adaptive fuzzy fault-tolerant consensus tracking controller is designed via adding one power integrator technique and directed graph theory so that the controlled systems are semiglobal practical finite-time stability (SGPFTS). Finally, numerical simulation results further verify the effectiveness of the developed control scheme.

Synchronization of Complex Dynamical Networks Subject to DoS Attacks: An Improved Coding-Decoding Protocol

This article investigates the synchronization of communication-constrained complex dynamic networks subject to malicious attacks. An observer-based controller is designed by virtue of the bounded encode sequence derived from an improved coding-decoding communication protocol. Moreover, taking the security of data transmission into consideration, the denial-of-service attacks with the frequency and duration characterized by the average dwell-time constraint are introduced into data communication, and their influence on the coder string is analyzed explicitly. Thereafter, by imposing reasonable restrictions on the transmission protocol and the occurrence of attacks, the boundedness of coding intervals can be obtained. Since the precision of data is generally limited, it may lead to the situation that the signal to be encoded overflows the coding interval such that it results in the unavailability of the developed coding scheme. To cope with this problem, a dynamic variable is introduced to the design of the protocol. Subsequently, based on the Lyapunov stability theory, sufficient conditions for ensuring the input-to-state stability of the synchronization error systems under the communication-constrained condition and malicious attacks are presented. The validity of the developed method is finally verified by a simulation example of chaotic networks.

Saturation-Tolerant Prescribed Control for a Class of MIMO Nonlinear Systems

This article proposes a saturation-tolerant prescribed control (SPC) for a class of multiinput and multioutput (MIMO) nonlinear systems simultaneously considering user-specified performance, unmeasurable system states, and actuator faults. To simplify the control design and decrease the conservatism, tunnel prescribed performance (TPP) is proposed not only with concise form but also smaller overshoot performance. By introducing non-negative modified signals into TPP as saturation-tolerant prescribed performance (SPP), we propose SPC to guarantee tracking errors not to violate SPP constraints despite the existence of saturation and actuator faults. Namely, SPP possesses the ability of enlarging or recovering the performance boundaries flexibly when saturations occur or disappear with the help of these non-negative signals. A novel auxiliary system is then constructed for these signals, which bridges the associations between input saturation errors and performance constraints. Considering nonlinearities and uncertainties in systems, a fuzzy state observer is utilized to approximate the unmeasurable system states under saturations and unknown actuator faults. Dynamic surface control is employed to avoid tedious computations incurred by the backstepping procedures. Furthermore, the closed-loop state errors are guaranteed to a small neighborhood around the equilibrium in finite time and evolved within SPP constraints although input saturations and actuator faults occur. Finally, comparative simulations are presented to demonstrate the feasibility and effectiveness of the proposed control scheme.

Adaptive Prescribed Performance Control of A Flexible-Joint Robotic Manipulator With Dynamic Uncertainties

An adaptive fuzzy control strategy is proposed for a single-link flexible-joint robotic manipulator (SFRM) with prescribed performance, in which the unknown nonlinearity is identified by adopting the fuzzy-logic system. By designing a performance function, the transient performance of the control system is guaranteed. To stabilize the SFRM, a dynamic signal is applied to handle the unmodeled dynamics. To cut down the communication load of the channel, the event-triggered control law is developed based on the switching threshold strategy. The Lyapunov stability theory and backstepping technique are applied coordinately to design the control strategy. The semiglobally ultimately uniformly boundedness can be ensured for all signals in the closed-loop system. The designed control method can also guarantee that the tracking error can converge to a small neighborhood of zero within the prescribed performance boundaries. At the end of the article, two illustrative examples are shown to validate the designed event-triggered controller.

Finite-Time Robust Intelligent Control of Strict-Feedback Nonlinear Systems With Flight Dynamics Application

The tracking control is investigated for a class of uncertain strict-feedback systems with robust design and learning systems. Using the switching mechanism, the states will be driven back by the robust design when they run out of the region of adaptive control. The adaptive design is working to achieve precise adaptation and higher tracking precision in the neural working domain, while the finite-time robust design is developed to make the system stable outside. To achieve good tracking performance, the novel prediction error-based adaptive law is constructed by considering the estimation performance. Furthermore, the output constraint is achieved by imbedding the barrier Lyapunov function-based design. The finite-time convergence and the uniformly ultimate boundedness of the system signal can be guaranteed. Simulation studies show that the proposed approach presents robustness and adaptation to system uncertainty.

Neural Adaptive Self-Triggered Control for Uncertain Nonlinear Systems With Input Hysteresis

The issue of neural adaptive self-triggered tracking control for uncertain nonlinear systems with input hysteresis is considered. Combining radial basis function neural networks (RBFNNs) and adaptive backstepping technique, an adaptive self-triggered tracking control approach is developed, where the next trigger instant is determined by the current information. Compared with the event-triggered control mechanism, its biggest advantage is that it does not need to continuously monitor the trigger condition of the system, which is convenient for physical realization. By the proposed controller, the hysteresis's effect can be compensated effectively and the tracking error can be bounded by an explicit function of design parameters. Simultaneously, all other signals in the closed-loop system can be remaining bounded. Finally, two examples are presented to verify the effectiveness of the proposed method.

Adaptive NN Finite-Time Resilient Control for Nonlinear Time-Delay Systems With Unknown False Data Injection and Actuator Faults

This article considers neural network (NN)-based adaptive finite-time resilient control problem for a class of nonlinear time-delay systems with unknown fault data injection attacks and actuator faults. In the procedure of recursive design, a coordinate transformation and a modified fractional-order command-filtered (FOCF) backstepping technique are incorporated to handle the unknown false data injection attacks and overcome the issue of "explosion of complexity" caused by repeatedly taking derivatives for virtual control laws. The theoretical analysis proves that the developed resilient controller can guarantee the finite-time stability of the closed-loop system (CLS) and the stabilization errors converge to an adjustable neighborhood of zero. The foremost contributions of this work include: 1) by means of a modified FOCF technique, the adaptive resilient control problem of more general nonlinear time-delay systems with unknown cyberattacks and actuator faults is first considered; 2) different from most of the existing results, the commonly used assumptions on the sign of attack weight and prior knowledge of actuator faults are fully removed in this article. Finally, two simulation examples are given to demonstrate the effectiveness of the developed control scheme.

H∞ Codesign for Uncertain Nonlinear Control Systems Based on Policy Iteration Method

In this article, the problem of H_∞ codesign for nonlinear control systems with unmatched uncertainties and adjustable parameters is investigated. The main purpose is to solve the adjustable parameters and H_∞ controller simultaneously so that better robust control performance can be achieved. By introducing a bounded function and defining a special cost function, the problem of solving the Hamilton-Jacobi-Isaacs equation is transformed into an optimization problem with nonlinear inequality constraints. Based on the sum of squares technique, a novel policy iteration algorithm is proposed to solve the problem of the H_∞ codesign. Moreover, one modified algorithm for optimizing the robust performance index is given. The convergence and the performance improvement of new iteration policy algorithms are proved. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Unmeasured Stochastic Nonlinear Systems With Unknown Control Directions

The issue of adaptive output-feedback stabilization is investigated for a category of stochastic nonstrict-feedback nonlinear systems subject to unmeasured state and unknown control directions. By combining the event-triggered mechanism and backstepping technology, an adaptive fuzzy output-feedback controller is devised. In order to make the controller design feasible, a linear state transformation is introduced into the initial system. At the same time, the Nussbaum function technology is used to overcome the difficulties caused by unknown control directions, and the state observer solves the problem of the unmeasured state. Based on the fuzzy-logic system and its structural characteristics, the issue of unknown nonlinear function with nonstrict-feedback structure in the system is tackled. The designed controller could not only guarantee all signals of closed-loop systems are bounded in probability but also save communication resources effectively. Finally, numerical simulation and ship dynamics example are given to confirm the effectiveness of the proposed method.

A fuzzy control algorithm for tracing air pollution based on unmanned aerial vehicles

The process of atmospheric pollutants traceability based on unmanned aerial vehicles (UAVs) is affected by many factors that can impact and increase the complexity of the traceability of atmospheric pollutants. In this study, we proposed a new algorithm called the fuzzy control traceability (FCT) to track odor plumes. Our proposed algorithm combined the characteristics and fuzzy control of the UAV and designed a controller based on the actual environment of the UAV. The fuzzy controller fuzzed the input gas concentration information, established fuzzy control rules by imitating human brain thinking, and outputted the turning angle and the move length according to rules, thus realizing intelligent tracking of the odor plume by the UAV. We compared the FCT algorithm with the bio-inspired "ZigZag" algorithm to validate its performance. Various concentration fields were constructed, and ten sets of experiments are performed using the two algorithms in different concentration fields. The average success rate of the FCT algorithm under different concentration fields was 95.4% higher than that of the ZigZag algorithm.Implications: Fuzzy control logic is applied to the field of air pollutant traceability of drones, and a single drone traceability algorithm based on fuzzy control is proposed; and in view of the shortcomings of a single traceability subject in the traceability, multiple traceability subjects are introduced to optimize fuzzy control.

Adaptive Fuzzy Finite-Time Control for Nonstrict-Feedback Nonlinear Systems

This article presents an adaptive fuzzy finite-time control (AFFTC) method for nonstrict-feedback nonlinear systems (NFNSs) with unknown dynamics. With the aid of the backstepping technique, by establishing the smooth switch function (SSF), a novel C¹ AFFTC strategy is recursively constructed, which counteracts the effect of nonstrict-feedback structure and unknown dynamics. Different from the reporting finite-time control achievements, the singularity hindrance derived from the differentiating virtual control law is availably surmounted. Moreover, the developed AFFTC strategy can drive the tracking error to converge into a small neighborhood of the origin in a finite time. Simulation results are conducted to substantiate the efficacy of theoretical findings.

Adaptive Learning and Sampled-Control for Nonlinear Game Systems Using Dynamic Event-Triggering Strategy

Static event-triggering-based control problems have been investigated when implementing adaptive dynamic programming algorithms. The related triggering rules are only current state-dependent without considering previous values. This motivates our improvements. This article aims to provide an explicit formulation for dynamic event-triggering that guarantees asymptotic stability of the event-sampled nonzero-sum differential game system and desirable approximation of critic neural networks. This article first deduces the static triggering rule by processing the coupling terms of Hamilton-Jacobi equations, and then, Zeno-free behavior is realized by devising an exponential term. Subsequently, a novel dynamic-triggering rule is devised into the adaptive learning stage by defining a dynamic variable, which is mathematically characterized by a first-order filter. Moreover, mathematical proofs illustrate the system stability and the weight convergence. Theoretical analysis reveals the characteristics of dynamic rule and its relations with the static rules. Finally, a numerical example is presented to substantiate the established claims. The comparative simulation results confirm that both static and dynamic strategies can reduce the communication that arises in the control loops, while the latter undertakes less communication burden due to fewer triggered events.

Fuzzy Adaptive Switching Control for Stochastic Systems With Finite-Time Prescribed Performance

The issue of fuzzy adaptive switching control for stochastic systems with arbitrary switching signal and finite-time prescribed performance is investigated in this article. A piecewise function is adopted to characterize finite-time prescribed performance, and the error signal is converted to a new state variable via the tangent function. Unknown functions are approximated via fuzzy-logic systems (FLSs). Based on the stochastic stability theory and common Lyapunov function, a fuzzy adaptive switching control scheme is presented. The control law is proposed for the stochastic switched closed-loop system so that not only all the signals are ensured to be semiglobally uniformly ultimately bounded (SGUUB) in probability but also a residual error related to the finite-time prescribed performance bound is guaranteed. Eventually, simulation studies for a practical system are given to show the effectiveness of the presented fuzzy adaptive switching control scheme.

A survey of adaptive optimal control theory

This paper makes a survey about the recent development of optimal control based on adaptive dynamic programming (ADP). First of all, based on DP algorithm and reinforcement learning (RL) algorithm, the origin and development of the optimization idea and its application in the control field are introduced. The second part introduces achievements in the optimal control direction, then we classify and summarize the research results of optimization method, constraint problem, structure design in control algorithm and practical engineering process based on optimal control. Finally, the possible future research topics are discussed. Through a comprehensive and complete investigation of its application in many existing fields, this survey fully demonstrates that the optimal control algorithms via ADP with critic-actor neural network (NN) structure, which also have a broad application prospect, and some developed optimal control design algorithms have been applied to practical engineering fields.

Global Finite-Time Stabilization for Uncertain Systems With Unknown Measurement Sensitivity

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

Neural-Network-Based Distributed Asynchronous Event-Triggered Consensus Tracking of a Class of Uncertain Nonlinear Multi-Agent Systems

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

Distributed Cooperative Compound Tracking Control for a Platoon of Vehicles With Adaptive NN

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

Finite-Time-Prescribed Performance-Based Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems With Dynamic Uncertainty and Actuator Faults

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.

Neuroadaptive Finite-Time Control for Nonlinear MIMO Systems With Input Constraint

This article considers the problem of finite-time (FT) tracking control for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with input backlash. A modified FT command filter is designed in each step of backstepping, which ensures the output of the filter can faster approximate the derivatives of virtual signals, suppress chattering, and relax the input signal limit of the Levant differentiator. Then, the corresponding improved FT error compensation mechanism is adopted to reduce the negative impact of filtering errors. Furthermore, a neural-network-adaptive technology is proposed for MIMO systems with input backlash via FT convergence. It is shown that desired tracking performance can be implemented in finite time. The simulation example is presented to illustrate the effectiveness and advantages of the new design method.

Adaptive Neural Fixed-Time Tracking Control for High-Order Nonlinear Systems

The problem of adaptive neural fixed-time tracking control for high-order systems is addressed in this article. In order to handle the difficulties from the uncertain nonlinearities within the original systems, the radial basis function neural networks (RBF NNs) are introduced to approximate the unknown nonlinear functions, and the adding a power integrator is applied to overcome the obstacle from high-order terms. It is proven that all signals in the closed-loop system are bounded and the output signal can eventually converge to a small neighborhood of the reference signal. Simulation results further verify the approaches developed.

Game-Based Backstepping Design for Strict-Feedback Nonlinear Multi-Agent Systems Based on Reinforcement Learning

In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

Adaptive Approximation-Based Tracking Control for a Class of Unknown High-Order Nonlinear Systems With Unknown Powers

In this article, the problem of adaptive tracking control is tackled for a class of high-order nonlinear systems. In contrast to existing results, the considered system contains not only unknown nonlinear functions but also unknown rational powers. By utilizing the fuzzy approximation approach together with the barrier Lyapunov functions (BLFs), we present a new adaptive tracking control strategy. Remarkably, the BLFs are employed to determine a priori the compact set for maintaining the validity of fuzzy approximation. The primary advantage of this article is that the developed controller is independent of the powers and can be capable of ensuring global stability. Finally, two illustrative examples are given to verify the effectiveness of the theoretical findings.

Event-triggered fuzzy filtering for nonlinear networked systems with dynamic quantization and stochastic cyber attacks

In this article, the H_∞ filtering issue is considered for discrete-time nonlinear networked systems subject to event-triggered communication scheme, dynamic quantization, and stochastic cyber attacks. The considered nonlinear networked system is described by the Takagi-Sugeno (T-S) fuzzy model. The event-triggered policy and the dynamic quantizer will be considered to realize the effective use of the restricted network bandwidth resources. Moreover, a stochastic variable that satisfies the Bernoulli random binary distribution is employed to characterize the effects of stochastic cyber attacks. This paper focus on the design of full- and reduced-order event-triggered H_∞ filters and the dynamic parameter of the quantizer such that the filtering error system is stochastically stable and satisfies a predefined H_∞ filtering performance. The sufficient design conditions for the event-triggered H_∞ filters and the dynamic parameter of the quantizer are proposed based on linear matrix inequalities (LMIs). Finally, an example based on practical application will be used to verify the effectiveness of the presented design methods.

Adaptive Neural Network Finite-Time Dynamic Surface Control for Nonlinear Systems

This article addresses the problem of finite-time neural network (NN) adaptive dynamic surface control (DSC) design for a class of single-input single-output (SISO) nonlinear systems. Such designs adopt NNs to approximate unknown continuous system functions. To avoid the "explosion of complexity" problem, a novel nonlinear filter is developed in control design. Under the framework of adaptive backstepping control, an NN adaptive finite-time DSC design algorithm is proposed by adopting a smooth projection operator and finite-time Lyapunov stable theory. The developed control algorithm means that the tracking error converges to a small neighborhood of origin within finite time, which further verifies that all the signals of the controlled system possess globally finite-time stability (GFTS). Finally, both numerical and practical simulation examples and comparing results are provided to elucidate the superiority and effectiveness of the proposed control algorithm.

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.