线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

Optimization of a Class of Nonlinear Dynamic Systems: New Efficient Method without Lagrange Multipliers

This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.     

A dynamic parameter estimator to control chaos with distinct feedback schemes

A dynamic strategy is proposed to estimate parameters of chaotic systems. The dynamic estimator of parameters can be used with diverse control functions; for example, those based on: (i) Lie algebra, (ii) backstepping, or (iii) variable feedback structure (sliding-mode). The proposal has adaptive structure because of interaction between dynamic estimation of parameters and a feedback control function. Without lost of generality, a class of dynamical systems with chaotic behavior is considered as benchmark. The proposed scheme is compared with a previous low-parameterized robust adaptive feedback in terms of execution and performance. The comparison is motivated to ask: What is the suitable adaptive scheme to suppress chaos in an specific implementation? Experimental results of proposed scheme are discussed in terms of control execution and performance and are relevant in specific implementations; for example, in order to induce synchrony in complex networks.     

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.     

Guaranteed Output Feedback Control for Uncertain Systems under Control and State Constraints

This paper deals with output feedback control of uncertain nonlinear dynamic systems in the presence of state and control constraints. We provide necessary and sufficient conditions for the guaranteed viability property defined by the existence of a Lipschitz closed-loop that maintains exactly the state of the system in a given closed domain of constraints despite some bounded disturbances acting both on the dynamics and on the output. Using the notion of Lipschitz kernel of a closed set-valued map, we obtain some equivalent geometric and Hamilton–Jacobi–Isaac conditions for the guaranteed viability property. We derive an algorithm to build a guaranteed viable output feedback.     

Output feedback regulation control for a class of cascade nonlinear systems and its application to fan speed control

The output feedback regulation problem is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics and unknown control direction. The system output together with the complete unmeasured state components appears in the system uncertainties. A systematic output feedback control scheme is presented with the help of a dynamic observer, whose gain comes from an off-line time-varying Riccati matrix differential equation. The proposed scheme can be applied to the analysis of the speed tracking control of a fan. The simulation results demonstrate the validity of the presented algorithm.     

一类非最小相位非线性系统的鲁棒输出调节

研究了一类具有非最小相位和非线性外部系统的非线性系统的全局鲁棒输出调节问题.首先,利用浸入系统设计了一个非线性内模.其次,把原系统的全局鲁棒输出调节问题转化为增广系统的全局鲁棒镇定问题.然后,利用改变能量函数和动态增益技巧设计了一个状态反馈控制器,使得闭环系统的解有界并且跟踪误差渐近趋于零.最后,利用仿真结果验证了所设计的控制器的有效性.     

Feedback control systems governed by evolution equations

ABSTRACT

The goal of this paper is to provide systematic approaches to study the feedback control systems governed by evolution equations in separable reflexive Banach spaces. We firstly give some existence results of mild solutions for the equations by applying the Banach's fixed point theorem and the Leray–Schauder alternative fixed point theorem with Lipschitz conditions and some types of boundedness conditions. Next, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence of feasible pairs for the feedback control systems. Some existence results for an optimal control problem are given. Finally, we apply our main result to obtain a controllability result for semilinear evolution equations and existence results for a class of differential variational inequalities and Clarke's subdifferential inclusions.     

一类非线性系统的迭代学习控制

讨论一类非线性系统的迭代学习控制,系统的非线性动态对状态不快于多项式增长,而量测方程含有噪声.控制序列并非直接输给系统,而是先经过死区、预载及饱和等非线性函数.递推地给出了学习控制序列,并证明它的有界性及最优跟踪性.     

Decentralized Control of Nonlinear Large-Scale Systems Using Dynamic Output Feedback

In this paper, a class of nonlinear large-scale systems with similar subsystems is studied. Both matched and unmatched uncertainties are considered by utilizing their bounding functions, and the interconnections take a more general form than considered previously. Based on a constrained Lyapunov equation, a nonlinear dynamic output feedback decentralized controller is presented. Unlike existing results, matched uncertainties are considered in the control design; by using a decomposition of the interconnections, the known and uncertain interconnections are treated separately; thus, the robustness is improved and conservativeness is reduced significantly. The computation effort for solving the Lyapunov equation is greatly reduced by taking into account the similar subsystem structure. Finally, simulation is used to illustrate the effectiveness of our results.     

Algebraic Multiplicities Arising from Static Feedback Control Systems of Parabolic Type

In stabilization studies of linear parabolic control systems, a successful approach is a scheme employing dynamic compensators in the feedback loop. An essential reason is the fact that both sensors and actuators cannot be designed freely, especially in the case of boundary observation/boundary feedback. Most fundamental in this scheme is a simple stabilization result under the static feedback control scheme. In this scheme, little attention has been paid to how to assign new eigenvalues of the feedback system. In this article, we show a new feature of pole assignment that shows some choices of new eigenvalues cause a deterioration of the stability property. An algebraic growth rate is added to the feedback system in such a choice.     

由发展算子确定的具有控制不等式约束的LQCP的最优反馈控制

研究由发展算子定义的具有控制函数积分不等式约束的线性二次控制问题（LQCP）,借助无约束线性二次控制系统推导出了最优控制的反馈形式。     

Application of stochastic artsteins theorem to feedback stablization

The stochastic Artstein's theorem is applied to derive sufficient conditions for dynamic asymptotic stabilization in probability by means of a feedback integrator for a class of nonlinear stochastic differential systems. A stabilizing feedback law is deduced from a control Lyapunov function     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.     

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and moving-horizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.     

An implicit systems characterization of a class of impulsive linear switched control processes. Part 1: Modeling

Our paper focuses on a fundamental structural property associated with a family of linear switched control systems in the presence of impulsive dynamics. We consider dynamic processes governed by piecewise linear ODEs with controlled location transitions and describe the resulting system in a constructive form of an implicit dynamic system. The proposed algebraic-based modeling framework follows the celebrated behavioral approach (see Polderman and Willems (1998)) and makes it possible to apply to the switched dynamics some conventional techniques from the well-established time-invariant implicit systems theory. The analytic results of our paper constitute a formal theoretical extension of switched control systems methodology and can be used (as an auxiliary step) in a concrete control design procedure. In this first part, we consider modeling aspects.     

广义系统动态输出反馈控制设计的新方法

对于连续时间的广义系统,基于线性矩阵不等式(LMI),提出了动态输出反馈H_∞控制设计的新方法.给出了广义系统动态输出反馈H_∞控制存在的充分条件.通过求解线性矩阵不等式和矩阵方程实现控制的设计.所提出确定控制的方法是简洁和易于实现的.一个数值例子说明了提出方法的设计过程和控制的有效性.     

Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control

In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, inequality techniques, some sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control and intermittent linear state delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.     

基于输出反馈的一类非线性不确定互联大系统的分散H∞控制

本文研究基于输出反馈的一类大型互联非线性不确定系统的分散H∞控制问题,通过构造每个子系统收敛的状态观测器,得到分散输出反馈控制器.当反馈控制律作用于该系统时,无扰动输入的闭环系统是全局渐近稳定的,而对允许的不确定性,干扰抑制的大小可以任意小,且控制器的设计也无需解任何的Hamilton-Jacobi方程或不等式.