H∞ control of nonlinear continuous-time systems based on dynamical fuzzy models

This paper presents a solution of the H_∞ control problem for a class of continuous-time nonlinear systems. The method is based on a fuzzy dynamical model of the nonlinear system. A suitable piecewise differentiate quadratic (PDQ) Lyapunov function is used to establish asymptotic stability of the closed-loop system. Furthermore, a constructive algorithm is developed to obtain the stabilizing feedback control law. The controller design algorithm involves solving a set of suitable algebraic Riccati equations. An example is given to illustrate the application of the method     

一类非线性系统的加权自校正控制

本文提出了仅含一个非线性环节的一类非线性系统控制的逆算子方法,建立了这类非线性系统的加权自校正控制算法。该算法也适用于不稳定和(或)逆不稳定系统,具有渐近最优控制效果,可以保证闭环系统全局稳定和收敛。仿真结果表明该算法能克服系统非线性的影响,改进了系统的控制性能。     

H∞ control for a class of cascade switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed‐loop system is globally asymptotically stable and has a prescribed H_∞ performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we study the hybrid H_∞ control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability analysis and H∞ control design for a class of nonlinear time‐delay systems

This paper investigates the stability and H_∞ control problem for a class of nonlinear time‐delay systems with a nonsingular Jacobian matrix, and provides a number of new results regarding stability analysis and control design. Firstly, an equivalent form is obtained for this class of systems by means of coordinate transformation and/or orthogonal decomposition of vector fields. Then, based on the equivalent form and free‐weighting matrix method, several sufficient conditions, in terms of nonlinear matrix inequalities, are derived for the stability analysis of the time‐delay systems by constructing suitable Lyapunov functionals. Finally, we use the equivalent form and the obtained stability results to investigate the H_∞ control problem, and present a control design procedure for this class of time‐delay systems. A study of illustrative examples shows that the results obtained in this paper have less conservatism, and work very well in the stability analysis and control design of some nonlinear time‐delay systems. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion (FSE) are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions (such as global Lipschitz c...     

SINGULARITY COMPUTATION FOR ITERATIVE CONTROL OF NONLINEAR AFFINE SYSTEMS

This paper considers a gradient type of iterative algorithm applied to the open loop control for nonlinear affine systems. The convergence of the algorithm relies on the control signal in each iteration be nonsingular. We present an algorithm for computing the singular control for a general class of nonlinear affine systems. Various nonlinear mechanical systems, including nonholonomic systems, are included as examples.     

On stabilization of nonlinear systems with enlarged domain of attraction

This paper presents a systematic procedure to design a control law that guarantees asymptotic stability of an equilibrium with an enlarged domain of attraction for a class of nonlinear systems. To this end, we use a natural extension of well-known linear time-invariant transformation methods to write the system in controller canonical form with a forcing term. The control law is implemented in two steps, first we calculate a nonlinear state feedback that cancels the nonlinear terms of the unforced system, so that for the resulting system a suitable Lyapunov function candidate is available. Then, we add a linear state feedback that stabilizes the equilibrium and maximizes its domain of attraction. Interestingly enough, the latter maximization problem reduces to a classical, linear time invariant H_∞ minimization problem. An example is given to illustrate the procedure.     

Robust H∞ Control for Non‐Minimum Phase Switched Cascade Systems with Time Delay

The H_∞ control of a class of the uncertain switched nonlinear cascaded systems with time delay is explored in this paper via the multiple Lyapunov functions. The considered systems are assumed to comprise an inherently nonlinear and a linearizable nonlinear dynamic system that may be non‐minimum phase. A group of partial differential inequalities containing adjustable functions are used in the control design task. The state feedback controllers and a suitable switching law are designed simultaneously so as to achieve the desired disturbance attenuation while preserving asymptotic stability for all admissible uncertainties. The partial differential inequalities are of lower dimension than general Hamilton–Jacobi inequalities, and therefore the solving process is feasible. This particular technique is applicable even if no subsystem is asymptotically stable. The non‐minimum phase property is compensated for by means of an appropriate switching mechanism. A robust H_∞ control for non‐switched cascade system with time delay is obtained in addition. An illustrative example is given to demonstrate the efficiency of the proposed design method.     

Adaptive Reliable <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control of Uncertain Affine Nonlinear Systems

For general input affine nonlinear systems, robust reliable control designs are commonly available that compensate the actuator faults in pure outage mode. In this paper, a more general and complex problem is considered and an adaptive reliable H_∞ controller is designed for a class of uncertain input affine nonlinear systems in the presence of actuators fault. The key element of the work is the introduction of a novel adaptive mechanism that estimates the faults which are modeled as an outage or loss of effectiveness and stabilizes the overall system. Incorporating with the parameter projection algorithm and the solution of Hamilton-Jacobi-Inequality (HJI), the proposed method combines adaptive reliable control and robust H_∞ control techniques. A numerical approach is developed based on the Taylor series expansion for solving the HJI. Various simulation examples are given to illustrate the effectiveness of the proposed adaptive reliable H_∞ control scheme over the conventional H_∞ control and reliable H_∞ control method.     

Robust H∞ Sliding Mode Control for a Class of Singular Stochastic Nonlinear Systems

This paper concerns the problem of robust H_∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H_∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results.     

Approximate dynamic programming for two-player zero-sum game related to <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of unknown nonlinear continuous-time systems

This paper develops a concurrent learning-based approximate dynamic programming (ADP) algorithm for solving the two-player zero-sum (ZS) game arising in H _∞ control of continuous-time (CT) systems with unknown nonlinear dynamics. First, the H _∞ control is formulated as a ZS game and then, an online algorithm is developed that learns the solution to the Hamilton-Jacobi-Isaacs (HJI) equation without using any knowledge on the system dynamics. This is achieved by using a neural network (NN) identifier to approximate the uncertain system dynamics. The algorithm is implemented on actor-critic-disturbance NN structure along with the NN identifier to approximate the optimal value function and the corresponding Nash solution of the game. All NNs are tuned at the same time. By using the idea of concurrent learning the need to check for the persistency of excitation condition is relaxed to simplified condition. The stability of the overall system is guaranteed and the convergence to the Nash solution of the game is shown. Simulation results show the effectiveness of the algorithm.     

A design technique for fast sampled-data nonlinear model predictive control with convergence and stability results

ABSTRACT

In this study, a sampled-data nonlinear model predictive control scheme is developed. The control algorithm uses a prediction horizon with variable length, a terminal constraint set, and a feedback controller defined on this set. Following a suboptimal solution strategy, a defined number of steps of an iterative optimisation routine improve the current input trajectory at each sampling point. The value of the objective function monotonically decreases and the state converges to a target set. A discrete-time formulation of the algorithm and a discrete-time design model ensure high computational efficiency and avoid an ad hoc quasi-continuous implementation. This design technique for a fast sampled-data nonlinear model predictive control algorithm is the main contribution of the paper. Based on a benchmark control problem, the performance of the developed control algorithm is assessed against state-of-the-art nonlinear model predictive control methods available in the literature. This assessment demonstrates that the developed control algorithm stabilises the system with very low computational effort. Hence, the algorithm is suitable for real-time control of fast dynamical systems.     

Modelling and control of nonlinear,operating point dependent systems via associative memory networks

This paper presents a novel approach to the modelling and control of a specific class of nonlinear systems whose parameters are unknown nonlinear functions of the measurable operating points. An associative memory network is used to identify each nonlinear function, whose inputs are the measurable operating points and output being the estimated value of the parameter. Two different cases are considered; the first being those systems where the networks can exactly model the nonlinear functions, whereas the second case considers those systems which can only approximate the nonlinear functions toa known accuracy. The first type of system is referred to as a matching system and the second is called a mismatching system. During the modelling phase, the weights for each network are trained in parallel using the normalised back-propagation algorithm for matching system, and the modified recursive least squares algorithm for mismatching systems. It has been shown that these algorithms together withGoodwin's technical lemma lead to a stable d-step-ahead control scheme for matching systems and a pole assignment control strategy for mismatching systems.     

Adaptive stabilization of a class of nonlinear systems using high-gain feedback

This note presents a high-gain feedback stabilizing control algorithm in which the high-gain parameter is adapted on-line. The algorithm is developed for a class of nonlinear systems which can be viewed as the nonlinear counterpart of uniform rank systems. The system can be unknown except for a number of vital pieces of information. For single-input single-output linear systems such information is usually required in the traditional adaptive control literature.     

基于神经网络的非线性学习控制研究

本文将多层前向传递神经网络应用于非线性系统控制,通过对神经网络的训练,实现非线性系统的状态反馈控制。本文还介绍了用神经网络控制一类非线性系统的学习控制算法,该算法对对象的数学模型依赖程度较低,为非线性系统的学习控制提供了一种有效的研究方法。另外还给出了该算法应用于几个不同非线性对象的学习控制仿真结果。     

一类非齐次时变线性模型及自适应预测控制策略

通过分析系统闭环预测存在的缺陷,为了改善系统的预测性能、便于系统辨识和实现自适应控制,提出了一类适合于一般非线性系统的非齐次时变线性模型,给出并证明了其存在性定理。而后给出了这类非齐次时变线性模型的渐消记忆递推最小二乘参数估计,推出了基于该类模型的自适应预测控制算法。仿真结果表明基于该类模型的自适应预测控制策略具有优良的控制品质。     

Robust nonlinear variable selective control for networked systems

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi–Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H₂ performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.     

ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

This paper proposes a convex approach to regional stability and ℒ︁₂‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁₂‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁₂‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

确定性Hammerstein模型的自适应控制算法及其全局收敛性

本文对广义的Hammerstein模型描述的一类非线性系统,提出一种复合的自适应控制算法.在适当的条件下,证明了这类非线性系统的稳定性和算法的全局收敛性.本文提出的算法可以适用于开环不稳定且具有"非最小相位"特性的系统.