Adaptive Neural Output-Feedback Decentralized Control for Large-Scale Nonlinear Systems With Stochastic Disturbances

Concurrent Learning-Based Adaptive Control of Underactuated Robotic Systems With Guaranteed Transient Performance for Both Actuated and Unactuated Motions

With the wide applications of underactuated robotic systems, more complex tasks and higher safety demands are put forward. However, it is still an open issue to utilize "fewer" control inputs to satisfy control accuracy and transient performance with theoretical and practical guarantee, especially for unactuated variables. To this end, for underactuated robotic systems, this article designs an adaptive tracking controller to realize exponential convergence results, rather than only asymptotic stability or boundedness; meanwhile, unactuated states exponentially converge to a small enough bound, which is adjustable by control gains. The maximum motion ranges and convergence speed of all variables both exhibit satisfactory performance with higher safety and efficiency. Here, a data-driven concurrent learning (CL) method is proposed to compensate for unknown dynamics/disturbances and improve the estimate accuracy of parameters/weights, without the need for persistency of excitation or linear parametrization (LP) conditions. Then, a disturbance judgment mechanism is utilized to eliminate the detrimental impacts of external disturbances. As far as we know, for general underactuated systems with uncertainties/disturbances, it is the first time to theoretically and practically ensure transient performance and exponential convergence speed for unactuated states, and simultaneously obtain the exponential tracking result of actuated motions. Both theoretical analysis and hardware experiment results illustrate the effectiveness of the designed controller.

Asymptotical Neuro-Adaptive Consensus of Multi-Agent Systems With a High Dimensional Leader and Directed Switching Topology

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

Decentralized Adaptive Neural Inverse Optimal Control of Nonlinear Interconnected Systems

Existing methods on decentralized optimal control of continuous-time nonlinear interconnected systems require a complicated and time-consuming iteration on finding the solution of Hamilton-Jacobi-Bellman (HJB) equations. In order to overcome this limitation, in this article, a decentralized adaptive neural inverse approach is proposed, which ensures the optimized performance but avoids solving HJB equations. Specifically, a new criterion of inverse optimal practical stabilization is proposed, based on which a new direct adaptive neural strategy and a modified tuning functions method are proposed to design a decentralized inverse optimal controller. It is proven that all the closed-loop signals are bounded and the goal of inverse optimality with respect to the cost functional is achieved. Illustrative examples validate the performance of the methods presented.

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.

Observer-Based Decentralized Control for Non-Strict-Feedback Fractional-Order Nonlinear Large-Scale Systems With Unknown Dead Zones

This article addresses the output-feedback decentralized control issue for the fractional-order nonlinear large-scale nonstrict-feedback systems with states immeasurable and unknown dead zones. The unknown nonlinear functions are identified by neural networks (NNs), and immeasurable states are estimated by establishing an NNs' decentralized state observer. The algebraic loop issue is solved by using the property of NN basis functions and designing the fractional-order adaptation laws. In addition, the fractional-order dynamic surface control (FODSC) design technique is introduced in the adaptive backstepping control algorithm to avoid the issue of "explosion of complexity." Then, by treating the nonsymmetric dead zones as the time-varying uncertain systems, an adaptive NNs' output-feedback decentralized control scheme is developed via the fractional-order Lyapunov stability criterion. It is proven that the controlled fractional-order systems are stable, and the tracking and observer errors can converge to a small neighborhood of zero. Two simulation examples are given to confirm the validity of the put forward control scheme.

Command filter-based adaptive fuzzy decentralized control for stochastic nonlinear large-scale systems with saturation constraints and unknown disturbance

In this article, the problem of decentralized fuzzy adaptive control is addressed for a class of stochastic interconnected nonlinear large-scale systems including saturation and unknown disturbance. Fuzzy logic systems (FLSs) are used to estimate packaged nonlinear uncertainties. The command filter technique is presented to eliminate the "explosion of complexity" obstacle associated with the backstepping procedures and the corresponding error compensation mechanism is constructed to alleviate the effect of the errors generated by command filters. The influence of input saturation is compensated by introducing an auxiliary system. Meanwhile, an improved adaptive fuzzy decentralized controller is developed and it is able to minimize calculation time since there is no need for repeated differentiation for the virtual control laws. The presented control scheme not only assures the semi-global boundedness of all the signals in the closed-loop system, but also makes the output tracking errors reach a small neighborhood around the origin. Finally, both numerical and practical examples are provided to illustrate the efficiency and effectiveness of our theoretic result.

Event-Triggered Adaptive Neural Network Control for Stochastic Nonlinear Systems With State Constraints and Time-Varying Delays

In this article, we pay attention to develop an event-triggered adaptive neural network (ANN) control strategy for stochastic nonlinear systems with state constraints and time-varying delays. The state constraints are disposed by relying on the barrier Lyapunov function. The neural networks are exploited to identify the unknown dynamics. In addition, the Lyapunov-Krasovskii functional is employed to counteract the adverse effect originating from time-varying delays. The backstepping technique is employed to design controller by combining event-triggered mechanism (ETM), which can alleviate data transmission and save communication resource. The constructed ANN control scheme can guarantee the stability of the considered systems, and the predefined constraints are not violated. Simulation results and comparison are given to validate the feasibility of the presented scheme.

Activated Gradients for Deep Neural Networks

Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this article, a novel method by acting the gradient activation function (GAF) on the gradient is proposed to handle these challenges. Intuitively, the GAF enlarges the tiny gradients and restricts the large gradient. Theoretically, this article gives conditions that the GAF needs to meet and, on this basis, proves that the GAF alleviates the problems mentioned above. In addition, this article proves that the convergence rate of SGD with the GAF is faster than that without the GAF under some assumptions. Furthermore, experiments on CIFAR, ImageNet, and PASCAL visual object classes confirm the GAF's effectiveness. The experimental results also demonstrate that the proposed method is able to be adopted in various deep neural networks to improve their performance. The source code is publicly available at https://github.com/LongJin-lab/Activated-Gradients-for-Deep-Neural-Networks.

Adaptive NN Optimal Consensus Fault-Tolerant Control for Stochastic Nonlinear Multiagent Systems

This article investigates the problem of adaptive neural network (NN) optimal consensus tracking control for nonlinear multiagent systems (MASs) with stochastic disturbances and actuator bias faults. In control design, NN is adopted to approximate the unknown nonlinear dynamic, and a state identifier is constructed. The fault estimator is designed to solve the problem raised by time-varying actuator bias fault. By utilizing adaptive dynamic programming (ADP) in identifier-critic-actor construction, an adaptive NN optimal consensus fault-tolerant control algorithm is presented. It is proven that all signals of the controlled system are uniformly ultimately bounded (UUB) in probability, and all states of the follower agents can remain consensus with the leader's state. Finally, simulation results are given to illustrate the effectiveness of the developed optimal consensus control scheme and theorem.

Event-Triggered Adaptive NN Tracking Control for MIMO Nonlinear Discrete-Time Systems

This article concentrates on the design of a novel event-based adaptive neural network (NN) control algorithm for a class of multiple-input-multiple-output (MIMO) nonlinear discrete-time systems. A controller is designed through a novel recursive design procedure, under which the dependence on virtual controls is avoided and only system states are needed. The numbers of the event-triggered conditions and parameters updated online in each subsystem reduce to only one, which largely reduces the computation burden and simplifies the algorithm realization. In this case, radial basis function NNs (RBFNNs) are employed to approximate the control input. The semiglobal uniformly ultimate boundedness (SGUUB) of all the signals in the closed-loop system is guaranteed by the Lyapunov difference approach. The effectiveness of the proposed algorithm is validated by a simulation example.

Adaptive Fuzzy Output-Feedback Decentralized Control for Fractional-Order Nonlinear Large-Scale Systems

This article studies the adaptive fuzzy output-feedback decentralized control problem for the fractional-order nonlinear large-scale systems. Since the considered strict-feedback systems contain unknown nonlinear functions and unmeasurable states, the fuzzy-logic systems (FLSs) are used to model unknown fractional-order subsystems, and a fuzzy decentralized state observer is established to obtain the unavailable states. By introducing the dynamic surface control (DSC) design technique into the adaptive backstepping control algorithm and constructing the fractional-order Lyapunov functions, an adaptive fuzzy output-feedback decentralized control scheme is developed. It is proved that the decentralized controlled system is stable and that the tracking and observer errors are able to converge to a neighborhood of zero. A simulation example is given to confirm the validity of the proposed control scheme.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

Command Filter-Based Adaptive Neural Control Design for Nonstrict-Feedback Nonlinear Systems With Multiple Actuator Constraints

This article proposes an adaptive neural-network command-filtered tracking control scheme of nonlinear systems with multiple actuator constraints. An equivalent transformation method is introduced to address the impediment from actuator nonlinearity. By utilizing the command filter method, the explosion of complexity problem is addressed. With the help of neural-network approximation, an adaptive neural-network tracking backstepping control strategy via the command filter technique and the backstepping design algorithm is proposed. Based on this scheme, the boundedness of all variables is guaranteed and the output tracking error fluctuates near the origin within a small bounded area. Simulations testify the availability of the designed control strategy.

Event-Triggered Adaptive Neural Network Sensor Failure Compensation for Switched Interconnected Nonlinear Systems With Unknown Control Coefficients

In this article, a decentralized adaptive neural network (NN) event-triggered sensor failure compensation control issue is investigated for nonlinear switched large-scale systems. Due to the presence of unknown control coefficients, output interactions, sensor faults, and arbitrary switchings, previous works cannot solve the investigated issue. First, to estimate unmeasured states, a novel observer is designed. Then, NNs are utilized for identifying both interconnected terms and unstructured uncertainties. A novel fault compensation mechanism is proposed to circumvent the obstacle caused by sensor faults, and a Nussbaum-type function is introduced to tackle unknown control coefficients. A novel switching threshold strategy is developed to balance communication constraints and system performance. Based on the common Lyapunov function (CLF) method, an event-triggered decentralized control scheme is proposed to guarantee that all closed-loop signals are bounded even if sensors undergo failures. It is shown that the Zeno behavior is avoided. Finally, simulation results are presented to show the validity of the proposed strategy.

Reduced-Order Filters-Based Adaptive Backstepping Control for Perturbed Nonlinear Systems

In this article, a robust adaptive output-feedback control approach is presented for a class of nonlinear output-feedback systems with parameter uncertainties and time-varying bounded disturbances. A reduced-order filter driven by control input is proposed to reconstruct unmeasured states. The state estimation error is shown to be bounded by dynamic signals driven by system output. The bound estimation technique is employed to estimate the unknown disturbance bound. Based on the backstepping design with three sets of tuning functions, an adaptive output-feedback control scheme with the flat-zone modification is proposed. It is shown that all the signals in the resulting closed-loop adaptive control systems are bounded, and the output tracking error converges to a prespecified small neighborhood of the origin. Two simulation examples are provided to illustrate the effectiveness and validity of the proposed approach.

Finite-Time Command-Filtered Composite Adaptive Neural Control of Uncertain Nonlinear Systems

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

Observer Design for Sampled-Data Systems via Deterministic Learning

A unified approach is proposed to design sampled-data observers for a certain type of unknown nonlinear systems undergoing recurrent motions based on deterministic learning in this article. First, a discrete-time implementation of high-gain observer (HGO) is utilized to obtain state trajectory from sampled output measurements. By taking the recurrent estimated trajectory as inputs to a dynamical radial basis function network (RBFN), a partial persistent exciting (PE) condition is satisfied, and a locally accurate approximation of nonlinear dynamics can be realized along the estimated sampled-data trajectory. Second, an RBFN-based observer consisting of the obtained dynamics from the process of deterministic learning is designed. Without resorting to high gains, the RBFN-based observer is shown capable of achieving correct state observation. The novelty of this article lies in that, by incorporating deterministic learning with the discrete-time HGO, the nonlinear dynamics can be accurately approximated along the estimated trajectory, and such obtained knowledge can then be utilized to realize nonhigh-gain state estimation for the same or similar sampled-data systems. Simulation is performed to validate the effectiveness of the proposed approach.

Data-Driven-Based Event-Triggered Control for Nonlinear CPSs Against Jamming Attacks

This brief considers the security control problem for nonlinear cyber-physical systems (CPSs) against jamming attacks. First, a novel event-based model-free adaptive control (MFAC) framework is established. Second, a multistep predictive compensation algorithm (PCA) is developed to make compensation for the lost data caused by jamming attacks, even consecutive attacks. Then, an event-triggering mechanism with the dead-zone operator is introduced in the adaptive controller, which can effectively save communication resources and reduce the calculation burden of the controller without affecting the control performance of systems. Moreover, the boundedness of the tracking error is ensured in the mean-square sense, and only the input/output (I/O) data are used in the whole design process. Finally, simulation comparisons are provided to show the effectiveness of our method.

Adaptive Neural-Network Controller for an Uncertain Rigid Manipulator With Input Saturation and Full-Order State Constraint

This article proposes an adaptive neural-network control scheme for a rigid manipulator with input saturation, full-order state constraint, and unmodeled dynamics. An adaptive law is presented to reduce the adverse effect arising from input saturation based on a multiply operation solution, and the adaptive law is capable of converging to the specified ratio of the desired input to the saturation boundary while the closed-loop system stabilizes. The neural network is implemented to approximate the unmodeled dynamics. Moreover, the barrier Lyapunov function methodology is utilized to guarantee the assumption that the control system works to constrain the input and full-order states. It is proved that all states of the closed-loop system are uniformly ultimately bounded with the presented constraints under input saturation. Simulation results verify the stability analyses on input saturation and full-order state constraint, which are coincident with the preset boundaries.

Fixed-Time Fuzzy Control for a Class of Nonlinear Systems

Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.

Security correction control of stochastic cyber-physical systems subject to false data injection attacks with heterogeneous effects

In this paper, the interconnected observer intervention-based security correction control idea is proposed for stochastic cyber-physical systems (CPSs) subjected to false data injection attacks (FDIAs). The FDIAs are injected into the controller-to-actuator channel by the adversary via wireless transmission. In particular, the FDIAs with heterogeneous effects are constructed, which consist of periodic attacks with unknown parameters and bias injection attacks with asymptotic convergence property. A novel interconnected adaptive observer structure is designed to online estimate the heterogeneous attack effects. The security correction control scheme with resilience is presented by integrating interconnected adaptive observer and robust technology. It is demonstrated that the impaired state signals can be corrected and desired security performance can be guaranteed for stochastic CPSs under FDIAs with heterogeneous effects. Finally, two simulation verifications, including a F-16 longitudinal dynamics system controlled by network, are established to verify the validity and feasibility for the presented strategy.

Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays

This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds.

Gradient Descent-Based Adaptive Learning Control for Autonomous Underwater Vehicles With Unknown Uncertainties

This article investigates the adaptive learning control problem for a class of nonlinear autonomous underwater vehicles (AUVs) with unknown uncertainties. The unknown nonlinear functions in the AUVs are approximated by radial basis function neural networks (RBFNNs), in which the weight updating laws are designed via gradient descent algorithm. The proposed gradient descent-based control scheme guarantees the semiglobal uniform ultimate boundedness (SUUB) of the system and the fast convergence of the weight updating laws. In order to reduce the computational burden during the backstepping control design process, the command-filter-based design technique is incorporated into the adaptive learning control strategy. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.

Event-Triggered Output-Feedback Control for Large-Scale Systems With Unknown Hysteresis

This article focuses on the event-triggered-based adaptive neural-network (NN) control problem for nonlinear large-scale systems (LSSs) in the presence of full-state constraints and unknown hysteresis. The characteristic of radial basis function NNs is utilized to construct a state observer and address the algebraic loop problem. To reduce the communication burden and the signal transmission frequency, the event-triggered mechanism and the encoding-decoding strategy are proposed with the help of a backstepping control technique. To encode and decode the event-triggering control signal, a one-bit signal transmission strategy is adopted to consume less communication bandwidth. Then, by estimating the unknown constants in the differential equation of unknown hysteresis, the effect caused by unknown backlash-like hysteresis is compensated for nonlinear LSSs. Moreover, the violation of full-state constraints is prevented based on the barrier Lyapunov functions and all signals of the closed-loop system are proven to be semiglobally ultimately uniformly bounded. Finally, two simulation examples are given to illustrate the effectiveness of the developed strategy.

Prescribed Performance Adaptive Neural Compensation Control for Intermittent Actuator Faults by State and Output Feedback

Due to the existing effects of intermittent jumps of unknown parameters during operation, effectively establishing transient and steady-state tracking performances in control systems with unknown intermittent actuator faults is very important. In this article, two prescribed performance adaptive neural control schemes based on command-filtered backstepping are developed for a class of uncertain strict-feedback nonlinear systems. Under the condition of system states being available for feedback, the state feedback control scheme is investigated. When the system states are not directly measured, a cascade high-gain observer is designed to reconstruct the system states, and in turn, the output feedback control scheme is presented. Since the projection operator and modified Lyapunov function are, respectively, used in the adaptive law design and stability analysis, it is proven that both schemes can not only ensure the boundedness of all closed-loop signals but also confine the tracking errors within prescribed arbitrarily small residual sets for all the time even if there exist the effects of intermittent jumps of unknown parameters. Thus, the prescribed system transient and steady-state performances in the sense of the tracking errors are established. Furthermore, we also prove that the tracking performance under output feedback is able to recover the tracking performance under state feedback as the observer gain decreases. Simulation studies are done to verify the effectiveness of the theoretical discussions.

Output-Feedback Flocking Control of Multiple Autonomous Surface Vehicles Based on Data-Driven Adaptive Extended State Observers

This article addresses an output-feedback flocking control problem for a swarm of autonomous surface vehicles (ASVs) to follow a leading ASV guided via a parameterized path. The leading and following ASVs are subject to completely unknown model parameters, external disturbances, and unmeasured velocities. A data-driven adaptive anti-disturbance control method is proposed for establishing a flocking behavior without any prior knowledge of model parameters. Specifically, a data-driven adaptive extended state observer (ESO) is proposed such that unknown input gains, unmeasured velocities, and total disturbance are simultaneously estimated. For the leading ASV, an output-feedback path-following control law is developed to follow a predefined parameterized path. For following ASVs, an output-feedback flocking control law is developed based on an artificial potential function for collision avoidance and connectivity preservation, in addition to a distributed ESO for estimating the velocity of the leading ASV through a cooperative estimation network. The simulation results are discussed to substantiate the efficacy of the proposed path-guided output-feedback ASV flocking control based on data-driven adaptive ESOs without measured velocity information.

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.

Observer-Based Adaptive Neural Networks Control for Large-Scale Interconnected Systems With Nonconstant Control Gains

In this article, an adaptive neural network (NN) decentralized output-feedback control design is studied for the uncertain strict-feedback large-scale interconnected nonlinear systems with nonconstant virtual and control gains. NNs are utilized to approximate the unknown nonlinear functions, and the immeasurable states are estimated via designing an NN decentralized state observer. By constructing the logarithm Lyapunov functions, an observer-based NN adaptive decentralized backstepping output-feedback control is developed in the framework of the decentralized backstepping control. The proposed adaptive decentralized backstepping output-feedback control can make that the closed-loop system is semiglobally uniformly ultimately bounded (SGUUB) and that the tracking and observer errors converge to a small neighborhood of the origin. The most important contribution of this article is that it removes the restrictive assumption in the existing results that both virtual and control gain functions in each subsystem must be constants. A numerical simulation example is provided to validate the effectiveness of the proposed control method and theory.

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

This article addresses the finite-time optimal control problem for a class of nonlinear systems whose powers are positive odd rational numbers. First of all, a finite-time controller, which is capable of ensuring the semiglobal practical finite-time stability for the closed-loop systems, is developed using the adaptive neural networks (NNs) control method, adding one power integrator technique and backstepping scheme. Second, the corresponding design parameters are optimized, and the finite-time optimal control property is obtained by means of minimizing the well-defined and designed cost function. Finally, a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.

Adaptive Fuzzy Sliding Mode Control for a Micro Gyroscope with Backstepping Controller

This paper developed an adaptive backstepping fuzzy sliding control (ABFSC) approach for a micro gyroscope. Based on backstepping design, an adaptive fuzzy sliding mode control was proposed to adjust the fuzzy parameters with self-learning ability and reject the system nonlinearities. With the Lyapunov function analysis of error function and sliding surface function, a comprehensive controller is derived to ensure the stability of the proposed control system. The proposed fuzzy control scheme does not need to know the system model in advance and could approximate the system nonlinearities well. The adaptive fuzzy control method has self-learning ability to adjust the fuzzy parameters. Simulation studies were implemented to prove the validity of the proposed ABFSMC strategy, showing that it can adapt to the changes of external disturbance and model parameters and has a satisfactory performance in tracking and approximation.

New Super-Twisting Zeroing Neural-Dynamics Model for Tracking Control of Parallel Robots: A Finite-Time and Robust Solution

Parallel robots are usually required to perform real-time tracking control tasks in the presence of external disturbances in the complex environment. Conventional zeroing neural-dynamics (ZNDs) provide an alternative solution for the real-time tracking control of parallel robots due to its capacity of parallel processing and nonlinearity handling. However, it is still a challenge for the solution in a unified framework of the ZND to deal with the external disturbances, and simultaneously possess a finite-time convergence property. In this paper, a novel ZND model by exploring the super-twisting (ST) algorithm, named ST-ZND model, is proposed. The theoretical analyses on the global stability, finite-time convergence, as well as the robustness against the external disturbances are rigorously presented. Finally, the effectiveness and superiority of the ST-ZND model for the real-time tracking control of parallel robots are demonstrated by two illustrative examples, comparisons, and convergence tests.

Finite-Time Fuzzy Control of Stochastic Nonlinear Systems

This paper studies the finite-time stabilization of a class of stochastic nonlinear systems. Different from functions which are necessarily known in the conventional finite-time control of nonlinear systems, the nonlinear functions can be completely unknown in this paper. By applying fuzzy-logic systems to approximate the unknown nonlinearities, a novel adaptive finite-time control strategy is proposed. However, due to the existence of approximation errors, the existing finite-time stability criterion cannot be used to analyze the stability of stochastic nonlinear systems. To deal with this difficulty, a finite-time stability criterion, by utilizing the mean value theorem of integrals, is first established in Lemma 5, which plays a significant role in the finite-time stability analysis of stochastic nonlinear systems. Then, the finite-time mean square stability of a stochastic nonlinear system is proved by combining Lemma 3 with Jensen's inequality.