Parameter identification and control of linear discrete-time systems

The parameter-adaptive self-organizing control of linear discrete-time systems is considered by designing dynamic feedback controllers which depend on the estimates of the parameters provided by an appropriate identifier. Two stochastic approximation algorithms for consistent identification of feedback systems are investigated and a condition of identifiability is presented. Then two controllers, one based on "overall" and another based on "per-interval" optimization, both depending on the output of the identifier, are discussed and their evaluations relative to the optimal are compared in illustrative examples.     

On-line identification and optimal control of continuous-time systems

In this paper, a moving algorithm for on-line identification of continuous-time systems is developed. With the proposed algorithm, the observed input–output data can be directly used to estimate the system parameters without any numerical pre-processing, and by means of a recursive formula the estimates can be updated step by step without repeatedly computing the matrix inversion. In this way, the use of both computer memory and computing time can be reduced. Besides, the computations are simple and straightforward. From the moving identification algorithm, a linear moving model can be obtained to represent the control systems. The on-line optimal control algorithm is also developed via the linear moving model. A slider-crank motion control system is used to illustrate that the proposed on-line identification and optimal control algorithms can give satisfactory results.     

Comments on "Parameter identification and control of linear discrete-time systems"

A new proof of convergence of the stochastic approximation algorithm for parameter identification of closed-loop linear discrete-time control systems is proposed. This algorithm relates very effectively in terms of a sufficient condition the stability properties of the closed-loop system with the convergence of the identification algorithms, which were previously treated independently.     

基于李雅普诺夫指数的离散混沌系统的控制研究

讨论了通过改变离散混沌系统的李雅普诺夫指数对离散混沌系统进行控制的一种方法。离散混沌系统的李雅普诺夫指数可按需要配置为负值，从而使系统收敛到任意的期望点上，仿真和实验结果表明，该控制方法是有效的，可以实现系统的快速稳定。     

New results on discrete-time delay systems identification

A new approach for simultaneous online identification of unknown time delay and dynamic parameters of discrete-time delay systems is proposed in this paper.The proposed algorithm involves constructing a new generalized regression vector and defining the time delay and the rational dynamic parameters in the same vector.The gradient algorithm is used to deal with the identification problem.The effectiveness of this method is illustrated through simulation.     

基于输入状态稳定的离散广义系统预测控制

针对一类具有持续扰动和输入约束的离散广义系统, 研究其鲁棒预测控制器的设计问题. 将输入状态稳定的概念引入广义系统预测控制, 在quasi-min-max 性能指标下, 提出了广义系统双模鲁棒预测控制器的设计方法, 证明了基于双模鲁棒预测控制器的闭环广义系统输入状态稳定, 且具有正则、因果性. 数值仿真结果验证了所提出方法的有效性.

     

On-line order estimation and parameter identification for linear stochastic feedback control systems (CARMA model)

This paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems (CARMA model) under the assumption that the upper bounds of system orders are known. The strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained. The estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients. The resulting closed-loop systems are then globally stable and the tracking sample mean square error is minimized as well. Simultaneously, the estimates of the adaptive tracking for orders and coefficients are also strongly consistent. The simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective.     

基于开环2闭环控制的离散动力系统同步研究

基于开环-闭环控制,提出了一种离散动力系统同步方法.系统地论述了该方法的基本原理,指出了该方法在实际应用中应注意的一系列问题.在此基础上,推导出为实现系统同步应采取控制策略的具体形式,并从理论上对其鲁棒性进行了论证.数字模拟结果表明,该方法不仅具有较高的同步效率,而且具有很强的适用性,能够在不同条件下实现两个同类或异类离散动力系统的同步.     

Active identification for discrete-time nonlinear control. II.Strict-feedback systems

For Part I, see ibid., vol. 47, no. 2, pp. 210-24 (2002). Presents a novel adaptive control design procedure for discrete-time nonlinear systems that can be transformed into the parametric-strict feedback form. This procedure utilizes the tools that were introduced in Part I, namely temporal separation of the parameter estimation task from the control task, the implementation of an active identification procedure through a recursive orthogonalized projection estimator and an input selection algorithm that guarantees complete identification in finite time. However, compared to the output-feedback case presented in Part I, the active identification task is now further complicated by the fact that the nonlinearities are allowed to depend on all states, not just the output. This requires a significant modification of the input selection procedure, which utilizes all the measured states to guarantee that the identification task will be completed in less time than in the output-feedback case     

Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function.

In this paper, two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed. In the beginning, the operation state space is divided into several subregions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the piecewise Lyapunov function, the stabilization criteria of the switching fuzzy system are derived. The criteria have two features: 1) the behavior of the two successive states of the system is considered in the inequalities and 2) the interactions among the fuzzy subsystems in each subregion Sj are presented by one matrix Xj. Due to the above two features, the feasible solutions of the inequalities in the criteria are much easier to be found. In other words, the criteria are much more relaxed than the existing criteria proposed in other literature. The proposed conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools. Two examples are given to present the superiority of the proposed criteria and the effectiveness of the fuzzy controller's design, respectively.     

Robust decentralized model reference adaptive control of discrete-time interconnected systems

A robust decentralized model reference adaptive controller is proposed for a class of large-scale systems composed of several interconnected subsystems and described by state space equations. We have formulated a local adaptive controller for each subsystem using only local information such that the state of this subsystem tracks the corresponding state of a reference model. The content of the paper is limited to interconnected subsystems which are described by linear, deterministic, single-input single-output and discrete-time models with unknown and/or slowly time-varying parameters. Sufficient conditions, formulated by utilizing Lyapunov theory, are given for the overall system to be stabilizable by decentralized state feedback adaptive control laws. The results are illustrated by a numerical example.     

Parametric identification of discrete-time SISO systems

The paper presents a method for the parametric identification of linear time-invariant discrete systems. The input and output data sequences of the system are initially transformed into information-bearing sequences of much lower order through the use of discrete Laguerre series. The parameter identification problem then becomes one of finding the solution to an overdetermined set of equations. Data transformation into the Laguerre spectrum is achieved through a fast and efficient computational algorithm which inherently possesses noise-reduction properties.     

Active identification for discrete-time nonlinear control. I.Output-feedback systems

The problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous-time case. In contrast, its discrete-time counterpart remains largely unexplored, primarily due to the difficulties associated with utilizing Lyapunov design techniques in a discrete-time framework. Existing results impose restrictive growth conditions on the nonlinearities to yield global stability. In this paper, we propose a novel approach, which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output-feedback canonical form, in which the nonlinearities depend only on the measured output, but are otherwise arbitrary. The main novelties of our design are: (i) the temporal and algorithmic separation of the parameter estimation task from the control task, and (ii) the development of an active identification procedure, which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters. We prove that our algorithm guarantees complete (for control purposes) identification in a finite time interval, whose maximum length we compute. Thus, the traditional structure of concurrent online estimation and control is replaced by a two-phase control strategy: first use active identification, and then utilize the acquired parameter information to implement any control strategy as if the parameters were known     

一类非线性离散时间系统的模糊辨识

对一类非线性离散时间系统提出了模糊辨识方法,此方法用与未知参数向量成线性关系的模糊逻辑系统作为辨识模型,并通过自适应学习律对此模糊逻辑系统中的未知参数进行自适应调节,文中证明了此方法可使辨识误差收敛到原点的一个邻域内。仿真结果验证了此方法的有效性。     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

区间时滞相关离散非线性系统的鲁棒模型预测控制

针对一类带有扰动、输入约束和凸多面体不确定性的区间时滞离散非线性系统, 提出一种鲁棒模型预测控制方法. 一方面, 利用min-max 模型预测控制求解鲁棒模型预测控制器, 以研究鲁棒预测控制在范数有界意义下的扰动抑制问题; 另一方面, 充分利用时滞的上下界信息构造Lyapunov 函数以得到控制器存在的充分条件. 最后给出了闭环系统鲁棒稳定性证明.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

基于最小二乘算法及神经网络的非线性离散系统的自适应控制

针对有关文献所设计的控制律，在一较弱的条件下，去掉了符号运算部分，证明该控制律可避免“零除”问题，提高了运算速度。对于这种基于神经网络和LS算法的自适应控制问题，证明了系统状态落入一紧集中，闭环系统的所有信号都是有界的，且系统输出和参考输出之间的跟踪误差收敛于以零为原点的某一有界球中。     

Effective digital implementation of fuzzy control systems based on approximate discrete-time models

This paper addresses an effective digital implementation of fuzzy control systems via an intelligent digital redesign (IDR) approach. The purpose of IDR is to effectively convert an existing continuous-time fuzzy controller to an equivalent sampled-data fuzzy controller in the sense of the state-matching. The authors show that, under reasonable assumptions, the IDR based on the exact discrete-time models can be reduced to the IDR based on the approximate discrete-time models. The state-matching error between the closed-loop trajectories is carefully analyzed using the integral quadratic functional approach. The estimation of the state-matching error is presented using the linear matrix inequality (LMI) techniques. The problem of designing the sampled-data fuzzy controller to minimize the estimation as well as to guarantee the stability is formulated and solved as the convex optimization problem with LMI constraints. It is also shown that the resulting sampled-data fuzzy controller recovers the performance of the continuous-time fuzzy controller as the sampling period approaches zero. A numerical example is used to demonstrate the effectiveness of the proposed design technique.