Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Neural network‐based adaptive dynamic surface control of uncertain nonlinear pure‐feedback systems

In this paper, by incorporating the dynamic surface control technique into a neural network‐based adaptive control design framework, we have developed a backstepping‐based control design for a class of nonlinear systems in pure‐feedback form with arbitrary uncertainty. The circular design problem which may exist in pure‐feedback systems is overcome. In addition, our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. A stability analysis is given, which shows that our control law can guarantee the semi‐global uniformly ultimate boundedness of the solution of the closed‐loop system, and makes the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict‐feedback nonlinear systems with arbitrary uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

Adaptive Neural Dynamic Surface Control for Stochastic Nonlinear Time‐Delay Systems with Input and Output Constraints

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.     

Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique

This paper investigates the problem of adaptive control for a class of stochastic nonlinear time‐delay systems with unknown dead zone. A neural network‐based adaptive control scheme is developed by using the dynamic surface control (DSC) technique and the minimal learning parameters algorithm. The dynamic surface control technique, which can avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, is first extended to the stochastic nonlinear time‐delay system with unknown dead zone. The unknown nonlinearities are approximated by the function approximation technique using the radial basis function neural network. For the purpose of reducing the numbers of parameters, which are updated online for each subsystem in the process of approximating the unknown functions, the minimal learning parameters algorithm is then introduced. Also, the adverse effects of unknown time‐delay are removed by using the appropriate Lyapunov–Krasovskii functionals. In addition, the proposed control scheme is systematically derived without requiring any information on the boundedness of the dead zone parameters and avoids the possible controller singularity problem in the approximation‐based adaptive control schemes with feedback linearization technique. It is shown that the proposed control approach can guarantee that all the signals of the closed‐loop system are bounded in probability, and the tracking errors can be made arbitrary small by choosing the suitable design parameters. Finally, a simulation example is provided to illustrate the performance of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

Adaptive practical preassigned finite‐time stability for a class of pure‐feedback systems with full state constraints

This paper focuses on an adaptive practical preassigned finite‐time control problem for a class of unknown pure‐feedback nonlinear systems with full state constraints. Two new concepts, called preassigned finite‐time function and practical preassigned finite‐time stability, are defined. In order to achieve the main result, the pure‐feedback system is first transformed into an affine strict‐feedback nonlinear system based on the mean value theorem. Then, an adaptive preassigned finite‐time controller is obtained based on a modified barrier Lyapunov function and backstepping technique. Finally, simulation examples are exhibited to demonstrate the effectiveness of the proposed scheme.     

Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation

In this paper, a robust adaptive fuzzy control approach is proposed for a class of nonlinear systems in strict‐feedback form with the unknown time‐varying saturation input. To deal with the time‐varying saturation problem, a novel controller separation approach is proposed in the literature to separate the desired control signal from the practical constrained control input. Furthermore, an optimized adaptation method is applied to the dynamic surface control design to reduce the number of adaptive parameters. By utilizing the Lyapunov synthesis, the fuzzy logic system technique and the Nussbaum function technique, an adaptive fuzzy control algorithm is constructed to guarantee that all the signals in the closed‐loop control system remain semiglobally uniformly ultimately bounded, and the tracking error is driven to an adjustable neighborhood of the origin. Finally, some numerical examples are provided to validate the effectiveness of the proposed control scheme in the literature.     

Tracking for nonlinear plants with multiple unknown time‐varying state delays using sliding mode with adaptation

In this paper, we develop a sliding mode model reference adaptive control (MRAC) scheme for a class of nonlinear dynamic systems with multiple time‐varying state delays, which is robust with respect to unknown plant delays, to a nonlinear perturbation, and to an external disturbance with unknown bounds. An appropriate Lyapunov–Krasovskii‐type functional is introduced to design the adaptation algorithms, and to prove stability. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive control for nonlinear cyber‐physical systems under false data injection attacks through sensor networks

This paper considers the adaptive control problem for a class of nonlinear cyber‐physical systems with unknown nonlinearities and false data injection attacks, where the sensors are corrupted by attackers. To mitigate the effects caused by the considered attacks, a novel coordinate transformation is developed in the backstepping control design. In addition, to deal with the multiple unknown time‐varying state feedback gains caused by the sensor attacks, the new types of Nussbaum functions are introduced in the adaptive control. By using Lyapunov stability theory, the proposed control scheme can guarantee all the closed‐loop system signals globally bounded. Finally, the examples demonstrate the effectiveness of the proposed method.     

Robust Adaptive Neural Control for a Class of Time‐Varying Delay Systems with Backlash‐like Hysteresis Input

This paper proposes a robust adaptive dynamic surface control (DSC) scheme for a class of time‐varying delay systems with backlash‐like hysteresis input. The main features of the proposed DSC method are that 1) by using a transformation function, the prescribed transient performance of the tracking error can be guaranteed; 2) by estimating the norm of the unknown weighted vector of the neural network, the computational burden can be greatly reduced; 3) by using the DSC method, the explosion of complexity problem is eliminated. It is proved that the proposed scheme guarantees all the closed‐loop signals being uniformly ultimately bounded. The simulation results show the validity of the proposed control scheme.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.