Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions

Tunnel Prescribed Control of Nonlinear Systems With Unknown Control Directions

This article solves the entry capture problem (ECP) such that for any initial tracking error, it can be regulated into the prescribed performance constraints within a user-given time. The challenge lies in how to remove the initial condition limitation and to handle the ECP for nonlinear systems under unknown control directions and asymmetric performance constraints. For better tracking performance, we propose a unified tunnel prescribed performance (TPP) providing strict and tight allowable set. With the aid of a scaling function, error self-tuning functions (ESFs) are then developed to make the control scheme suitable to any initial condition (including the initial constraint violation), where the initial values of ESFs always satisfy performance constraints. In lieu of the Nussbaum technique, an orientation function is introduced to deal with unknown control directions while such way is capable of reducing the control peaking problem. Using ESFs, together with TPP and an orientation function, the resulted tunnel prescribed control (TPC) leads to a solution for the underlying ECP, which also exhibits a low complexity level since no command filters or dynamic surface control is required. Finally, simulation results are provided to further demonstrate these theoretical findings.

Finite-time prescribed performance tracking control for nonlinear time-delay systems with state constraints and actuator hysteresis

In this paper, the problem of adaptive neural network prescribed performance tracking control for a class of non-strict feedback time-delay systems constrained by full-state is studied. Radial basis function (RBF) neural networks (NNs) are integrated into the backstepping medium to deal with the uncertain functions and the barrier Lyapunov function (BLF) technique ensures that the state of the system does not exceed its limits. Subsequently, integrated with the Lyapunov-Krasovskii functional, the proposed control scheme makes the tracking errors converge to the preset region while the state constraint is not violated. Finally, the effectiveness of the scheme is supported by two simulation experiments.

Neural Network-Based Adaptive Tracking Control for Denitrification and Aeration Processes With Time Delays

Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov-Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.

Event-Triggered Adaptive Fuzzy Neural Network Output Feedback Control for Constrained Stochastic Nonlinear Systems

This article investigates the problem of command-filtered event-triggered adaptive fuzzy neural network (FNN) output feedback control for stochastic nonlinear systems (SNSs) with time-varying asymmetric constraints and input saturation. By constructing quartic asymmetric time-varying barrier Lyapunov functions (TVBLFs), all the state variables are not to transgress the prescribed dynamic constraints. The command-filtered backstepping method and the error compensation mechanism are combined to eliminate the issue of "computational explosion" and compensate the filtering errors. An FNN observer is developed to estimate the unmeasured states. The event-triggered mechanism is introduced to improve the efficiency in resource utilization. It is shown that the tracking error can converge to a small neighborhood of the origin, and all signals in the closed-loop systems are bounded. Finally, a physical example is used to verify the feasibility of the theoretical results.

Dynamic Gain Reduced-Order Observer-Based Global Adaptive Neural-Network Tracking Control for Nonlinear Time-Delay Systems

In this article, a globally adaptive neural-network tracking control strategy based on the dynamic gain observer is proposed for a class of uncertain output-feedback systems with unknown time-varying delays. A reduced-order observer with novel dynamic gain is proposed. An n th-order continuously differentiable switching function is constructed to achieve the continuous switching control of the system, thus further ensuring that all the closed-loop signals are globally uniformly ultimately bounded (GUUB). It is proved that by adjusting the designed parameters, the tracking error converges to a region which can be adjusted to be small enough. The effectiveness of the control scheme is demonstrated by two simulation examples.

Performance Improvement of Active Suspension Constrained System via Neural Network Identification

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

Adaptive Iterative Learning Control for a Class of Nonlinear Strict-Feedback Systems With Unknown State Delays

In this article, an adaptive iterative learning control scheme is presented for a class of nonlinear parametric strict-feedback systems with unknown state delays, aiming to achieve the point-wise tracking of desired trajectory in a finite interval. The appropriate Lyapunov-Krasovskii functions are established to compensate the influence of time-delay uncertainties on the control systems. As the main features, the proposed approach integrates the command filter into the backstepping procedure to avoid the differential explosion problem that may occur with the increase of system order, and introduces the hyperbolic tangent functions into the learning controller to handle the singularity problem thus maintaining the continuity of input signal. The results of theoretical analysis and numerical simulation demonstrate that the tracking errors at the entire period will converge to a compact set along the iteration axis. Compared with the existing works, the proposed control scheme is promising to manifest the better performance and practicability owing to the learning mechanism, the dynamic model, as well as the implementation of controller.

Deterministic learning-based neural control for output-constrained strict-feedback nonlinear systems

This paper studies learning from adaptive neural control of output-constrained strict-feedback uncertain nonlinear systems. To overcome the constraint restriction and achieve learning from the closed-loop control process, there are several significant steps. Firstly, a state transformation is introduced to convert the original constrained system output into an unconstrained one. Then an equivalent n-order affine nonlinear system is constructed based on the transformed unconstrained output state in norm form by the system transformation method. By combining dynamic surface control (DSC) technique, an adaptive neural control scheme is proposed for the transformed system. Then all closed-loop signals are uniformly ultimately bounded and the system output tracks the expected trajectory well with satisfying the constraint requirement. Secondly, the partial persistent excitation condition of the radial basis function neural network (RBF NN) could be verified to achieve. Therefore, the uncertain dynamics can be precisely approximated by RBF NN. Subsequently, the learning ability of RBF NN is achieved, and the knowledge acquired from the neural control process is stored in the form of constant neural networks (NNs). By reutilizing the knowledge, a novel learning controller is established to improve the control performance when facing the similar or same control task. The proposed learning control (LC) scheme can avoid repeating the online adaptation of neural weight estimates, which saves computing resources and improves transient performance. Meanwhile, the LC method significantly raises the tracking accuracy and the speed of error convergence while satisfying of the constraint condition simultaneously. Simulation studies demonstrate the efficiency of this proposed control scheme.

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.

Adaptive composite dynamic surface neural control for nonlinear fractional-order systems subject to delayed input

In the article, the adaptive composite dynamic surface neural controller design problem for nonlinear fractional-order systems (NFOSs) subject to delayed input is discussed. A fractional-order auxiliary system is first designed to solve the input-delay problem. By using the developed novel estimation models, the defined prediction errors and the states of error system can decide the weights of radial basis function neural networks (RBFNNs). During the dynamic surface controller design process, the developed fractional-order filters are designed to handle the complexity explosion problem when the classical backstepping control technique is utilized. It is shown that the designed adaptive composite neural controller ensures that all the system state variables are bounded and the tracking error of the considered system finally tends to a small neighborhood of zero. Finally, the results of the simulation explain the feasibility of the developed controller. In addition, the developed controller can also be applied to single input and single output(SISO) nonlinear systems subject to a unitary input function.

Adaptive tracking control for stochastic nonlinear systems with time-varying delays using multi-dimensional Taylor network

For stochastic nonlinear systems (SNSs) perturbed by compound uncertainties, the conventional model-based control approaches assume that the evolution behavior of uncertain variables is known. Unfortunately, such approaches are often conservative for most practical scenarios with the slow convergence speed and unsatisfactory anti-interference performance. For this sake, an adaptive control scheme based on deep deterministic policy gradient (DDPG) and multi-dimensional Taylor network (MTN) is proposed here to address the tracking problem for a category of SNSs subject to fast time-varying uncertainties, stochastic disturbance and unknown time-varying delays. The effect of time delay is embedded in the reproducing kernel Hilbert space through the error coordinate transformation. In the framework of DDPG, the MTN-based surrogate is utilized to construct the online network and target network via the temporal-difference method, which promises more desirable real-time performance due to its concise structure than conventional NN-based surrogates. In order to enhance the robustness of the system under fast time-varying uncertainties, a novel persistent excitation (PE) mechanism is designed to ensure that the control policy is appropriately rewarded or punished. Based on the PE condition, weights of MTNs converge exponentially and animate the system to evolve towards the target persistently. The tracking error and closed-loop state signals are proved theoretically to be uniformly ultimately bounded (UUB) via Lyapunov-Krasovskii functional. A numerical simulation from the process industry verifies the effectiveness of the proposed method.

IBLF-Based Adaptive Neural Control of State-Constrained Uncertain Stochastic Nonlinear Systems

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

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.

Fault-Tolerant Adaptive Fuzzy Tracking Control for Nonaffine Fractional-Order Full-State-Constrained MISO Systems With Actuator Failures

The problem of fault-tolerant adaptive fuzzy tracking control against actuator faults is investigated in this article for a type of uncertain nonaffine fractional-order nonlinear full-state-constrained multi-input-single-output (MISO) system. By means of the existence theorem of the implicit function and the intermediate value theorem, the design difficulty arising from nonaffine nonlinear terms is surmounted. Then, the unknown ideal control inputs are approximated by using some suitable fuzzy-logic systems. An adaptive fuzzy fault-tolerant control (FTC) approach is developed by employing the barrier Lyapunov functions and estimating the compounded disturbances. Moreover, under the drive of the reference signals, a sufficient condition ensuring semiglobal uniform ultimate boundedness is obtained for all the signals in the closed-loop system, and it is proved that all the states of nonaffine nonlinear fractional-order systems are guaranteed to remain inside the predetermined compact set. Finally, two numerical examples are provided to exhibit the validity of the designed adaptive fuzzy FTC approach.

Anti-Saturation-Based Adaptive Sliding-Mode Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

Adaptive NN Controller of Nonlinear State-Dependent Constrained Systems With Unknown Control Direction

Various constraints commonly exist in most physical systems; however, traditional constraint control methods consider the constraint boundaries only relying on constant or time variable, which greatly restricts applying constraint control to practical systems. To avoid such conservatism, this study develops a new adaptive neural controller for the nonlinear strict-feedback systems subject to state-dependent constraint boundaries. The nonlinear state-dependent mapping is employed in each step of backstepping procedure, and the prescribed transient performance on tracking error and the constraints on system states are ensured without repeatedly verifying the feasibility conditions on virtual controllers. The radial basis function neural network (NN) with less parameters approach is introduced as an identifier to estimate the unknown system dynamics and reduce computation burden. For removing the effect of unknown control direction, the Nussbaum gain technique is integrated into controller design. Based on the Lyapunov analysis, the developed control strategy can ensure that all the closed-loop signals are bounded, and the constraints on full system states and tracking error are achieved. The simulation examples are used to illustrate the effectiveness of the developed control strategy.

Distributed Fuzzy Adaptive Output-Feedback Control of Unknown Nonlinear Multiagent Systems in Strict-Feedback Form

This article is concerned with the cooperative tracking control problem for heterogeneous multiagent systems in a leader-following form under a directed graph. The dynamics of each following agent is unknown, obeying a strict-feedback form. With the help of fuzzy-logic systems, input filters, and constraint-handling schemes, a fully distributed output-feedback control algorithm is proposed to achieve output synchronization with prescribed performance and guarantee boundedness of signals in the closed-loop systems. In addition, the algorithm exhibits a simplicity control attribute in the sense that: 1) the control design utilizes only relative output measurements, and no extra information needs to be transmitted via the network and 2) the issue of explosion of complexity is addressed, without employing command filters or dynamic surface control techniques. Finally, the simulation results clarify and verify the established theoretical findings.

Neural-Network-Based Adaptive Event-Triggered Asymptotically Consensus Tracking Control for Nonlinear Nonstrict-Feedback MASs: An Improved Dynamic Surface Approach

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It's important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of ``complexity explosion'' in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.

Adaptive Tracking Control for Perturbed Strict-Feedback Nonlinear Systems Based on Optimized Backstepping Technique

In this article, an adaptive optimized control scheme based on neural networks (NNs) is developed for a class of perturbed strict-feedback nonlinear systems. An optimized backstepping (OB) technique is employed for breaking through the limitation of the matching condition. The disturbance of existing nonlinear systems may degrade system performance or even lead to instability. In order to improve the system's robustness, a disturbance observer is constructed to compensate for the impact coming from the external disturbance. Because the proposed optimized scheme needs to train the adaptive parameters not only for reinforcement learning (RL) but also for the disturbance observer, it will become more challenging no matter designing the control algorithm or deriving the adaptive updating laws. Finally, by virtue of the Lyapunov stability theory, it is proved that all internal signals of the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the validity of the devised method.

Adaptive Neural Digital Control of Hysteretic Systems With Implicit Inverse Compensator and Its Application on Magnetostrictive Actuator

Hysteresis is a complex nonlinear effect in smart materials-based actuators, which degrades the positioning performance of the actuator, especially when the hysteresis shows asymmetric characteristics. In order to mitigate the asymmetric hysteresis effect, an adaptive neural digital dynamic surface control (DSC) scheme with the implicit inverse compensator is developed in this article. The implicit inverse compensator for the purpose of compensating for the hysteresis effect is applied to find the compensation signal by searching the optimal control laws from the hysteresis output, which avoids the construction of the inverse hysteresis model. The adaptive neural digital controller is achieved by using a discrete-time neural network controller to realize the discretization of time and quantizing the control signal to realize the discretization of the amplitude. The adaptive neural digital controller ensures the semiglobally uniformly ultimately bounded (SUUB) of all signals in the closed-loop control system. The effectiveness of the proposed approach is validated via the magnetostrictive-actuated system.

Adaptive Asymptotic Regulation for Uncertain Nonlinear Stochastic Systems with Time-Varying Delays

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

NN Reinforcement Learning Adaptive Control for a Class of Nonstrict-Feedback Discrete-Time Systems

This article investigates an adaptive reinforcement learning (RL) optimal control design problem for a class of nonstrict-feedback discrete-time systems. Based on the neural network (NN) approximating ability and RL control design technique, an adaptive backstepping RL optimal controller and a minimal learning parameter (MLP) adaptive RL optimal controller are developed by establishing a novel strategic utility function and introducing external function terms. It is proved that the proposed adaptive RL optimal controllers can guarantee that all signals in the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). The main feature is that the proposed schemes can solve the optimal control problem that the previous literature cannot deal with. Furthermore, the proposed MPL adaptive optimal control scheme can reduce the number of adaptive laws, and thus the computational complexity is decreased. Finally, the simulation results illustrate the validity of the proposed optimal control schemes.

Robust Adaptive Fault-Tolerant Tracking Control for Nonaffine Stochastic Nonlinear Systems With Full-State Constraints

In this article, the adaptive fault-tolerant tracking control problem of nonaffine stochastic nonlinear systems with actuator failures and full-state constraints is studied. To surmount the design difficulty from nonaffine nonlinear term with multi-input and single-output (MISO) faulty modes, a novel nonlinear fault compensation function with adjustable parameter factor is first introduced to establish a standard adaptive fault-tolerant control (AFTC) strategy based on the mean-value theorem. Then, the remaining nonlinear function, including the partial loss of effectiveness, outage, and stuck cases, together with the constructed compound nonlinear function can be approximated by using the suitable fuzzy-logic system (FLS). Moreover, it is shown that all the states of nonaffine stochastic nonlinear systems are not violating the preset constraint bounds by employing the barrier Lyapunov functions (BLFs). Also, the given adaptive controller can guarantee all the closed-loop signals are uniformly ultimately bounded (UUB) in probability in the sense of fourth-moment within the appropriate compact sets. Finally, two simulation examples are given to demonstrate the validity of the proposed method.

Adaptive Neural Control of a Class of Stochastic Nonlinear Uncertain Systems With Guaranteed Transient Performance

In this paper, an adaptive neural network control for stochastic nonlinear systems with uncertain disturbances is proposed. The neural network is considered to approximate an uncertain function in a nonlinear system. And computational burden in operation is reduced by handling the norm of the neural-network vector. However, it will arise chattering issue, which is a challenge to avoid it from the symbolic operation. Further, traditional schemes often view error of estimate as bounded constant, but it is a time-varying function exactly, which may lead control schemes cannot conform to practical situation and guarantee stability of systems. Thus, backstepping technology and the neural network technology combined to stabilize stochastic nonlinear systems together to handle the aforementioned issues. It is proved that the proposed control scheme can guarantee the satisfactory asymptotic convergence performance and predetermined transient tracking error performance. From simulation results, the proposed control scheme is verified that can guarantee the satisfactory effectiveness.

Adaptive Neural Command Filtering Control for Nonlinear MIMO Systems With Saturation Input and Unknown Control Direction

In this paper, the tracking control problem is considered for a class of multiple-input multiple-output (MIMO) nonlinear systems with input saturation and unknown direction control gains. A command filtered adaptive neural networks (NNs) control method is presented with regard to the MIMO systems by designing the virtual controllers and error compensation signals. First, the command filtering is used to solve the "explosion of complexity" problem in the conventional backstepping design and the nonlinearities are approximated by NNs. Then, the error compensation signals are developed to conquer the shortcoming of the dynamic surface method. In addition, the Nussbaum-type functions are utilized to cope with the unknown direction control gains. The effectiveness of the proposed new design scheme is illustrated by simulation examples.

Adaptive Decentralized Controller Design for a Class of Switched Interconnected Nonlinear Systems

This paper is concerned with the switched decentralized adaptive control design problem for switched interconnected nonlinear systems under arbitrary switching, where the actuator failures may occur infinite times and the control directions are allowed to be unknown. By introducing a Nussbaum-type function and an integrable auxiliary signal, a switched decentralized adaptive control scheme is developed to deal with the potentially infinite times of actuator failures and the unknown control directions. The basic idea is to design different parameter update laws and control laws for distinct switched subsystems. It is proved that the state variables of the resulting closed-loop system are asymptotically stable. Finally, a numerical simulation on a double-inverted pendulum model is given to verify the proposed control scheme.

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

This paper addresses the problem of adaptive neural output-feedback decentralized control for a class of strongly interconnected nonlinear systems suffering stochastic disturbances. An state observer is designed to approximate the unmeasurable state signals. Using the approximation capability of radial basis function neural networks (NNs) and employing classic adaptive control strategy, an observer-based adaptive backstepping decentralized controller is developed. In the control design process, NNs are applied to model the uncertain nonlinear functions, and adaptive control and backstepping are combined to construct the controller. The developed control scheme can guarantee that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded in fourth-moment. The simulation results demonstrate the effectiveness of the presented control scheme.

Further Results on Adaptive Stabilization of High-Order Stochastic Nonlinear Systems Subject to Uncertainties

This paper concerns the adaptive state-feedback control for a class of high-order stochastic nonlinear systems with uncertainties including time-varying delay, unknown control gain, and parameter perturbation. The commonly used growth assumptions on system nonlinearities are removed, and the adaptive control technique is combined with the sign function to deal with the unknown control gain. Then, with the help of the radial basis function neural network approximation approach and Lyapunov-Krasovskii functional, an adaptive state-feedback controller is obtained through the backstepping design procedure. It is verified that the constructed controller can render the closed-loop system semiglobally uniformly ultimately bounded. Finally, both the practical and numerical examples are presented to validate the effectiveness of the proposed scheme.

Adaptive NN Control Without Feasibility Conditions for Nonlinear State Constrained Stochastic Systems With Unknown Time Delays

In the novel, an adaptive neural network (NN) controller is developed for a category of nonlinear stochastic systems with full state constraints and unknown time delays. The control quality and system stability suffer from the problems of state time delays and constraints which frequently arises in most real plants. The considered systems are transformed into new constrained free systems based on nonlinear mappings, such that full state constraints are never violated and the feasibility conditions on virtual controllers (the values of virtual controllers and its derivative are assumed to be known) are removed. To compensate for unknown time delayed uncertainties, the exponential type Lyapunov-Krasovskii functionals (LKFs) are employed. NNs are utilized to approximate unknown nonlinear functions appearing in the design procedure. In addition, by employing dynamic surface control (DSC) technique and less adjustable parameters, the online computation burden is lightened. The control method presented can achieve the semiglobal uniform ultimate boundedness of all the closed-loop system signals and the satisfactions of full state constraints by rigorous proof. Finally, by presenting simulation examples, the efficiency of the presented approach is revealed.

Neural Network Controller Design for a Class of Nonlinear Delayed Systems With Time-Varying Full-State Constraints

This paper proposes an adaptive neural control method for a class of nonlinear time-varying delayed systems with time-varying full-state constraints. To address the problems of the time-varying full-state constraints and time-varying delays in a unified framework, an adaptive neural control method is investigated for the first time. The problems of time delay and constraint are the main factors of limiting the system performance severely and even cause system instability. The effect of unknown time-varying delays is eliminated by using appropriate Lyapunov-Krasovskii functionals. In addition, the constant constraint is the only special case of time-varying constraint which leads to more complex and difficult tasks. To guarantee the full state always within the time-varying constrained interval, the time-varying asymmetric barrier Lyapunov function is employed. Finally, two simulation examples are given to confirm the effectiveness of the presented control scheme.

Small-Gain Technique-Based Adaptive NN Control for Switched Pure-Feedback Nonlinear Systems

This paper focuses on the problem of adaptive neural networks (NNs) tracking control for a class of completely nonaffine switched pure-feedback uncertain nonlinear systems with switched reference model. A sufficient and necessary condition for the control problem to be solvable is derived by exploiting the common Lyapunov function (CLF) method, backstepping, input-to-state stability analysis, and the small-gain technique. Also, a small-gain technique-based adaptive NN control scheme is provided to avoid the designed difficulty caused by the construction of an overall CLF for the switched closed-loop system, which is usually required when studying the switched pure-feedback system. Adaptive NN controllers of individual subsystems are constructed to guarantee that all of the signals in the closed-loop system are semi-globally uniformly ultimately bounded under arbitrary switchings, and the tracking error converges to a small neighborhood of the origin. Two examples, which include a continuously stirred tank reactor system, are presented to demonstrate the effectiveness of the proposed design approach.

Neural Learning Control of Strict-Feedback Systems Using Disturbance Observer

This paper studies the compound learning control of disturbed uncertain strict-feedback systems. The design is using the dynamic surface control equipped with a novel learning scheme. This paper integrates the recently developed online recorded data-based neural learning with the nonlinear disturbance observer (DOB) to achieve good "understanding" of the system uncertainty including unknown dynamics and time-varying disturbance. With the proposed method to show how the neural networks and DOB are cooperating with each other, one indicator is constructed and included into the update law. The closed-loop system stability analysis is rigorously presented. Different kinds of disturbances are considered in a third-order system as simulation examples and the results confirm that the proposed method achieves higher tracking accuracy while the compound estimation is much more precise. The design is applied to the flexible hypersonic flight dynamics and a better tracking performance is obtained.

Neural Networks-Based Adaptive Control for Nonlinear State Constrained Systems With Input Delay

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

Adaptive Neural Tracking Control of Switched Stochastic Pure-Feedback Nonlinear Systems With Unknown Bouc-Wen Hysteresis Input

This paper aims to analyze the problem of adaptive neural network (NN) tracking control for a class of switched stochastic nonlinear pure-feedback systems with unknown direction hysteresis. In the light of recent studies on the hysteresis phenomenon in the field of nonlinear switched systems, this paper focuses on Bouc-Wen hysteresis model with unknown parameters and direction conditions. To simplify the control design, the following procedure is applied. Prior to tackling the unknown direction hysteresis problem based on the Nussbaum function and the backstepping techniques, the pure-feedback structure difficulty is governed by the mean value theorem. Furthermore, an optimized adaptation method is utilized to cope with computational burden. Universal approximation capability of radial basis function NNs and Lyapunov function method is synthesized to develop an adaptive NN tracking control scheme. It is demonstrated that under arbitrary deterministic switching, the presented controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a neighborhood of the origin. Finally, two simulation examples are given to illustrate the advantages of the proposed control design approach.

Adaptive Fault-Tolerant Control for Nonlinear Systems With Multiple Sensor Faults and Unknown Control Directions

This paper investigates the problem of adaptive fault-tolerant control for a class of nonlinear parametric strict-feedback systems with multiple unknown control directions. Multiple sensor faults are first considered such that all real state variables are unavailable. Then, a constructive design method for the problem is set up by exploiting a parameter separation and regrouping technique. To circumvent the main obstacle caused by the coupling effects of multiple unknown control directions and sensor faults, a region-dependent segmentation analysis method is proposed. It is proven that the closed-loop system is globally exponentially stable. Simulation results are presented to illustrate the effectiveness of the proposed scheme.