Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

非线性扩展结构大系统自适应神经网络跟踪控制

针对一类非线性关联大系统在结构扩展时的跟踪控制问题, 提出一种采用自适应神经网络的控制方法. 该方法要求在不改变原结构系统控制律的前提下设计新加入子系统的控制律和自适应律, 使扩展后所有子系统都具有很好的跟踪性能. 这里主要利用神经网络的逼近功能以及Backstepping 技术来设计自适应律和控制律, 通过Lyapunov 理论证明在该控制器的作用下闭环系统的所有信号均是有界的, 并可使系统准确跟踪. 仿真结果验证了所提出方法的有效性.

     

Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems

A globally stable decentralized adaptive backstepping neural network tracking control scheme is designed for a class of large‐scale systems with mismatched interconnections. Under the assumption that the subsystems share the reference signals from the other subsystems, neural networks are used to approximate the unknown interconnections dependent on all reference signals such that the NN approximation domain can be determined a priori based on the bounds of reference signals. The proposed control approach can guarantee that all closed‐loop signals are globally uniformly ultimately bounded and that the tracking errors converge to a small residual set around the origin. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

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.     

Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems

In this paper, the decentralized adaptive neural network (NN) output‐feedback stabilization problem is investigated for a class of large‐scale stochastic nonlinear strict‐feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed‐loop system can be proved to be stable in probability by constructing an overall state‐quartic and parameter‐quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

A piecewise linear system consists of a set of linear time‐invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single‐input, single‐output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed‐loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.     

Adaptive control for a class of high‐order switched nonlinearly parameterized systems

The problem of adaptive stabilization is studied for a class of high‐order switched nonlinearly parameterized systems; none of subsystems is assumed to be adaptively stabilizable. By exploiting the multiple Lyapunov functions method and the adding a power integrator technique, a switched adaptive control technique is set up. Meanwhile, in order to reduce the conservativeness caused by adoption of a common update law for all subsystems, different update laws of individual subsystems are designed. Also, we simultaneously construct a switching law and adaptive state‐feedback controllers of subsystems to achieve global stability in the sense of Lyapunov of the closed‐loop system and global asymptotic regulation of the system states. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

NN-adaptive output feedback tracking control for a class of discrete-time non-affine systems with a dynamic compensator

The problem of tracking control for a class of uncertain non-affine discrete-time nonlinear systems with internal dynamics is addressed. The fixed point theorem is first employed to ensure the control problem in question is solvable and well-defined. Based on it, an adaptive output feedback control scheme based on neural network (NN) is presented. The proposed control algorithm consists of two parts: a dynamic compensator is introduced to stabilise the linear portion of the tracking error system; a single-hidden-layer neural network (SHL NN) approximation mechanism is introduced to cancel the uncertainties resulting from the non-affine function, where the recursive weight update rules of NN estimation are derived from the discrete-time version of Lyapunov control theory. Ultimate boundedness of the error signals is shown through Lyapunov’s direct method and the discrete-time version of input-to-state stability (ISS) theory. Finally, a model of automatical underwater vehicle (AUV) is considered to show the effectiveness of the proposed control scheme.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

基于事件触发的离散 MIMO 系统自适应评判容错控制

本文针对具有执行器故障的一类离散非线性多输入多输出(Multi-input multi-output, MIMO)系统, 提出了一种基于事件触发的自适应评判容错控制方案. 该控制方案包括评价和执行网络. 在评价网络里, 为了缓解现有的非光滑二值效用函数可能引起的执行网络跳变问题, 利用高斯函数构建了一个光滑的效用函数, 并采用评价网络近似最优性能指标函数. 在执行网络里, 通过变量替换将系统状态的将来信息转化成关于系统当前状态的函数, 并结合事件触发机制设计了最优跟踪控制器. 该控制器引入了动态补偿项, 不仅能够抑制执行器故障对系统性能的影响, 而且能够改善系统的控制性能. 稳定性分析表明所有信号最终一致有界且跟踪误差收敛于原点的有界小邻域内. 数值系统和实际系统的仿真结果验证了该方案的有效性.     

Full state constraints-based adaptive control for switched nonlinear pure-feedback systems

This paper investigates the problem of full state constraints-based adaptive control for a class of switched nonlinear pure-feedback systems under arbitrary switchings. First, the switched pure-feedback system is transformed into a switched strict-feedback system with non-affine terms based on the mean value theorem. Then, by exploiting the common Lyapunov function (CLF) method, the Barrier Lyapunov function method and backstepping, state feedback controllers of individual subsystems and a common Barrier Lyapunov function (CBLF) are constructed, which guarantee that all signals in the closed-loop system are global uniformly bounded under arbitrary switchings, and full state constraints are not violated. Furthermore, the tracking error can converge to a bounded compact set. Two examples, which include a single-link robot as a practical example, are provided to demonstrate the effectiveness of the proposed design method.     

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.     

Input/output‐to‐state stability for switched nonlinear systems with unstable subsystems

In this paper, a couple of sufficient conditions for input/output‐to‐state stability (IOSS) of switched nonlinear systems with non‐IOSS subsystems are derived by exploiting the multiple Lyapunov functions (MLFs) method. A state‐norm estimator–based small‐gain theorem is also established for switched interconnected nonlinear systems under some proper switching laws, where the small‐gain property of individual connected subsystems is not required in the whole state space instead only in some subregions of the state space. The state‐norm estimator for the switched system under study is explicitly designed via a constructive procedure by exploiting the MLFs method and the classical small‐gain technique. The presented results permit removal of a technical condition in existing literature, where all subsystems in switched systems are IOSS or some are IOSS. An illustrative example is also provided to illustrate the effectiveness of the theoretical results.     

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.     

Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback

The essence of intelligence lies in the acquisition/learning and utilization of knowledge. However, how to implement learning in dynamical environments for nonlinear systems is a challenging issue. This article investigates the deterministic learning (DL) control problem for uncertain pure‐feedback systems by output feedback, which achieves the human‐like learning and control in a simple way. To reduce the complexity of control design and analysis, first, by combining an appropriate system transformation, the original pure‐feedback system is transformed into a simple normal nonaffine system. An observer is then introduced to estimate the transformed system states. Based on the backstepping and dynamic surface control techniques, a simple adaptive neural control scheme is first developed to guarantee the finite time convergence of the tracking error using only one neural network (NN) approximator. Second, through DL, the exponential convergence of the NN weights is obtained with the satisfaction of partial persistent excitation condition. Thus, locally accurate approximation/learning of the transformed unknown system dynamics is achieved and stored as constant NNs. Finally, by utilizing the stored knowledge, an experience‐based controller is constructed and a novel learning control scheme is further proposed to improve the control performance without any further adaptation online for the estimate neural weights. Simulation results have been given to illustrate that the proposed scheme not only can learn and memorize knowledge like humans but also can utilize experience to achieve superior control performance.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.