一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

The sector bound approach to quantized feedback control

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

1IntroductionBifurcation control has attracted great attention in thepast two decades[1].The study of bifurcation control atpresent mostly concerns bifurcation stabilization,delay ofthe onset of aninherent bifurcation,changingthe parametervalue of an existing bifurcation point,and so on[1~4].Fromthe stability point of view,a bifurcation point of anonlinear systemis very disadvantageous.Asystemthat hasa bifurcation point may have more than one equilibriumpoint in a neighborhood of the bifurcati…     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator, which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.     

Generalized invariant subspaces and parameter insensitivedisturbance-rejection problems with static output feedback

In the geometric approach some generalized invariant subspaces for uncertain linear systems are investigated, and then various parameter insensitive disturbance-rejection problems with static output feedback are formulated and necessary and sufficient conditions for the problems to be solvable are presented. Further, some sufficient conditions which are useful to check the solvability conditions are presented using the notions of generalized invariant subspaces     

Output regulation of linear plants subject to constraints

Output regulation problems for continuous-time linear systems with state and/or input constraints are studied. The problems are formulated in global and semi-global setting by using state or full information feedback. The goal of this paper is to develop solvability conditions for the posed problems. Moreover, appropriate regulators are constructed under the solvability conditions. To state the solvability conditions clearly, a taxonomy of constraints is introduced which delineates the constraints into several categories. Such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable. Results developed here include as a special case the results obtained in the literature for systems with only input constraints. The constraint taxonomy also identifies some intrinsically hard constraints (non-right invertible constraints) for which the solvability conditions of global/semi-global output regulation problems are not clear yet. As a special case of output regulation, we also consider tracking problems with constraints. It is shown that if there exists a state feedback controller with a stabilizing domain of attraction, then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain.     

Quadratic stability and stabilization of bimodal piecewise linear systems

This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

Decentralized control: a stable proper fractional approach

Three decentralized control problems are considered in a fractional setup for two-channel multivariable systems. All three problems are instances of decentralized control or local output feedback problems. The problems are: (i) making the system stabilizable and detectable through the first channel via dynamic output feedback around the second channel, (ii) the first problem with the constraint of internal stability, and (iii) the decentralized stabilization problem. All three problems are equivalent as far as the solvability conditions are concerned. A characterization of all solutions in each case is given. The results apply to a class of systems having fractional representations over an arbitrary principal ideal domain     

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.     

Semi‐global stabilization of discrete‐time systems subject to non‐right invertible constraints

This paper investigates time‐invariant linear systems subject to input and state constraints. We study discrete‐time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non‐right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time‐invariant linear systems with non‐right invertible constraints, necessary and sufficient conditions are developed under which semi‐global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd.     

Structure invariance for uncertain nonlinear systems

A unified study of three control problems associated to multi-input multi-output nonlinear systems with uncertainties is presented, namely, input-state linearization by static state feedback, input-output decoupling by static state feedback and input-output decoupling by dynamic compensation. For each of these problems, geometric conditions which describe intrinsic structural invariance properties are given     

基于输出反馈的不确定连续系统的鲁棒预测控制

运用线性矩阵不等式方法,研究一类基于输出反馈的线性连续时间范数有界参数不确定系统的鲁棒预测控制问题．基于变量变换的思想,将无限时域“最小—最大”优化问题转化为线性规划问题,得出分段连续的输出反馈控制律,并给出了控制律存在的充分条件,证明了优化问题在初始时刻的可行解保证闭环系统渐近稳定．仿真实例验证了此方法的有效性．     

一般非线性系统的控制解耦

本文利用微分几何方法,讨论了一般非线性系统的反馈解耦和无交互控制问题,给出了一般非线性系统的状态方程反馈解耦及块输入-块输出无交互控制问题可解的充分必要条件.     

The decoupling of generalized state-space systems via statefeedback

The input-output decoupling problem of generalized state-space systems (GSS) via proportional state feedback is studied. The following three major issues are resolved: the necessary and sufficient conditions for the problem to have a solution, the general analytical expressions of the controller matrices, and the general analytical expressions of the diagonal elements of the closed-loop system. It is concluded that the approach presented seems to be a quite powerful tool for solving several feedback design problems for GSS systems. Using this method, problems such as decoupling and simultaneous pole assignment and decoupling via output feedback are successfully studied     

Sufficient LMI conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems

In this note, sufficient conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H/sub /spl infin// output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H/sub /spl infin// output feedback control and simultaneous H/sub /spl infin// output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.     

The interpretation of discontinuous state feedback control laws as nonanticipative control strategies in differential games

In differential games, one player chooses a feedback strategy to maximize a payoff. The other player counters by applying a minimizing open loop control. Classical notions of feedback strategies, based on state feedback control laws for which the corresponding closed loop dynamics uniquely define a state trajectory, are too restrictive for many problems, owing to the absence of minimizing classical feedback strategies or because consideration of classical feedback strategies fails to define, in a useful way, the value of the game. A number of feedback strategy concepts have been proposed to overcome this difficulty. That of Elliot and Kalton, according to which a feedback strategy is a nonanticipative mapping between control functions for the two players, has been widely taken up because it provides a value of the game which connects, via the Hamilton-Jacobi-Isaacs equation, with other fields of systems science. Heuristic analysis of specific games problems often points to discontinuous optimal feedback strategies. These cannot be regarded as classical feedback control strategies because the associated state trajectories are not in general unique. We give general conditions under which they can be interpreted as generalized feedback strategies in the sense of Elliot and Kalton.     

不确定奇异大系统分散鲁棒预测控制

针对一类不确定奇异关联大系统,讨论了当系统状态不可测时,基于输出反馈的分散鲁棒预测控制问题.通过构造Lyapunov函数以及应用线性矩阵不等式方法,将"min-max"优化问题转化为凸优化问题求解,从而得到了输出反馈分散控制器存在的充分条件和显示表达式.证明了优化问题在初始时刻的可行解能保证奇异闭环大系统渐近稳定且正则无脉冲.仿真结果验证了算法的有效性.     

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach.     

广义系统极点配置的一种代数几何方法

利用代数几何方法给出了可任意配置极点的条件,并证明了实数域上广义系统若存在复 反馈配置极点,则一定存在实反馈配置极点.