状态和控制含多时滞的离散系统H∞容错控制

针对状态和控制输入同时具有多个时滞的线性离散时间系统,基于Lyapunov稳定性理论和线性矩阵不等式方法(LMI),采用无时滞记忆的状态反馈控制律,研究了执行器故障情况下,离散多时滞系统的H∞容错控制问题.在采用连续执行器故障模型条件下,给出了系统没有干扰输入时存在无时滞记忆的状态反馈容错控制器的充分条件;进一步,给出了在H∞扰动衰减指标约束下,系统存在无时滞记忆的状态反馈H∞容错控制器的充分条件,并将结论推广到离散故障模型的情况.仿真结果证明了所提H∞容错控制器设计方法的正确性和有效性.     

Markov切换系统的随机稳定性分析

根据混合系统离散状态的动态行为和Markov链的状态也是离散的特点,提出了一类离散状态的动态行为是Markov链的混合系统。与传统的混合系统相比,这类系统能够刻画出混合系统离散动态行为的随机性,可以用来描述系统受到外界环境因素制约和内部突发事件等随机因素影响而发生变化的动态行为。根据动态系统的稳定性定义以及随机过程理论,给出了Markov线性切换系统的随机稳定性定义,并且分析了Markov线性切换系统的随机稳定性问题,给出了判定随机稳定性的充分必要条件。     

基于二维混合模型的改进型重复控制器设计

针对一类线性系统,提出一种基于连续/离散二维混合模型的改进型重复控制系统设计方法.首先,通过分析重复控制系统中独立存在的控制行为和学习行为,建立了连续/离散二维混合模型,并将重复控制设计问题转化为一类连续/离散二维系统的状态反馈控制问题;然后,基于对重复控制过程的分析和二维模型,提出一种新型重复控制系统结构,并将重复控制器的设计问题转化为连续/离散二维混合系统的状态反馈设计问题;最后,应用二维Lyapunov泛函理论和线性矩阵不等式方法,获得了重复控制器参数求解方法.     

基于混合信号的状态估计方法

传统的系统状态估计方法只用到连续信号,而离散测量信号所包含的信息没有得到利用.提出一种基于混合信号(包括连续和离散)的系统状态估计方法,既利用了连续信号,也用到离散信号的信息.该方法将离散信号的变化视作系统的离散事件,提取其准确的信息并参与系统状态估计,构成具有混合系统特性的新型状态估计器.还讨论了该估计器的稳定性条件和设计方法.仿真实验证明这种所提出的状态估计方法可以有效地改善系统的状态估计性能.     

混合系统的广义预测控制(GPC)及稳定性分析

被控对象为连续系统，控制器采用离散的广义预测控制器(GPC)。从而构成一个混合系统，给出此系统的传递函数计算公式，从而推导出幅值域度和相角域度，并且应用线性矩阵不等式(LMI)方法，分析整个闭环系统的稳定性。从而得出闭环系统具较强的鲁捧性。     

具有有界控制输入的状态反馈控制系统闭环稳定性

本文基于李雅普诺夫定理,给出了具有有界控制输入的离散时间系统和连续时间控制系统的闭环渐近稳定性判据。利用不考虑控制约束时闭环系统李雅普诺夫矩阵方程解,得出了当控制输入有界时,线性状态反馈控制系统为渐近稳定的充分条件。这些判据具有简单的形式,并且易于计算。     

具有干扰输入的离散广义系统有限时间控制器设计

主要研究具有干扰输入的离散线性广义系统有限时间状态稳定问题,首先讨论离散广义自治系统有限时间状态有界性问题,做为推论,给出了无外部干扰离散广义系统有限时间稳定条件,这些问题可解的充分条件以线性矩阵不等式(LMI)形式给出。     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

基于二维混合模型的改进型重复控制器设计

针对一类线性系统,提出一种基于连续/离散二维混合模型的改进型重复控制系统设计方法.首先,通过分析重复控制系统中独立存在的控制行为和学习行为,建立了连续/离散二维混合模型,并将重复控制设计问题转化为一类连续/离散二维系统的状态反馈控制问题;然后,基于对重复控制过程的分析和二维模型,提出一种新型重复控制系统结构,并将重复控制器的设计问题转化为连续/离散二维混合系统的状态反馈设计问题;最后,应用二维Lyapunov 泛函理论和线性矩阵不等式方法,获得了重复控制器参数求解方法.

     

冷连轧混合系统中离散事件仿真的建模及关键技术

本文以冷连轧过程仿真为例，分析了混合系统中离散事件的特点以及与连续部分的关 系，对系统进行了层次化分解，讨论了在混合系统仿真过程中对于离散事件部分的建模需要 注意的问题，同时给出了用有限状态机方法实现仿真建模的过程，以及实际应用中的关键技 术．     

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

This paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.     

多模式网络化控制系统稳定性分析

网络传输引起的时滞在网络化控制系统中经常出现．针对存在多个运动模式的网络化控制系统,建立了时滞混杂自动机模型,分析了系统平衡点的稳定性,给出了平衡点保持稳定的充分条件在于构造的与离散状态相关的Lyapunov泛函在离散状态的切换时刻是非增的．当时滞混杂自动机中连续性子系统为线性时不变时滞系统时,可以利用线性矩阵不等式方法来寻找系统的公共Lyapunov泛函,并求解使系统平衡点保持稳定的时滞上界．最后,给出了一个例子说明了分析结果．     

Design of linear observers for a class of linear hybrid systems

This paper deals with the design of linear observers for a class of linear hybrid systems. Such systems are composed of continuous-time and digital substates and possess, in general, coupling dynamics between both substates. Two observer prototypes based on the prediction error are proposed. The first is based on the observation of an extended discrete system at sampling instants. The discrete extended state is composed of the sampled values of the continuous substate at sampling instants and the digital substate. The estimation of the continuous substate in between sampling instants is made by using the plant parametrization and the sampled prediction error at the preceding sampling instant. The continuous-time state estimates are reinitialized at each new sampling instant by taking values from the corresponding components of the discretized substate of the observer of the auxiliary discrete extended system. The second observer prototype estimates the continuous-time substate for all time from initial conditions which are taken only when the estimation algorithm starts. The observer involves feedback information of the current observation error, that of the preceding sampling instant and that associated with the estimation of the discrete system. As a result, the discontinuities of the estimated substate at sampling instants, which typically occur with the use of the first prototype, are not present in this observation scheme. The exponential convergence to zero of both prediction and observation errors may be ensured under observability and detectability assumptions Furthermore, prescribed pole placement of the state estimation error is achieved under observability of the discrete extended plant. Also, prescribed pole placement of the combined dynamics of the extended plant and observation error can be obtained. For that purpose, the extended hybrid plant is assumed to be controllable when the linear control input is generated from measurements of the state observation. in both observation prototypes.     

Span-reachability and observability of bilinear hybrid systems

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics are determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and span-reachability in terms of rank conditions for generalized observability and controllability matrices. This characterization is useful for the system theory of bilinear hybrid systems, in particular, it is used in the realization theory of bilinear hybrid systems, (Petreczky, 2006).     

State estimation for linear hybrid systems with periodic jumps and unknown inputs

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.     

基于二维混合模型和状态观测器的重复控制设计

针对一类正则线性系统, 提出一种基于状态观测器和二维混合模型的重复控制系统设计方法. 首先, 通过构造一个状态观测器来重构系统的状态, 建立基于重构状态的线性控制律. 然后, 通过独立地考虑重复控制系统的连续控制过程与离散学习行为, 给出基于状态观测器和重构状态反馈的连续/离散二维混合模型. 针对这个混合模型, 运用二维Lyapunov泛函方法, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出重复控制系统存在重复控制器和状态观测器的充分条件, 所给条件可用Matlab工具箱方便地求解. 数值仿真验证了本文所提方法的有效性.     

Strongly Regular Differential Variational Systems

A differential variational system is defined by an ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution of a finite-dimensional variational inequality containing the state variable of the system. This paper addresses two system-theoretic topics for such a nontraditional nonsmooth dynamical system; namely, (non-)Zenoness and local observability of a given state satisfying a blanket strong regularity condition. For the former topic, which is of contemporary interest in the study of hybrid systems, we extend the results in our previous paper, where we have studied Zeno states and switching times in a linear complementarity system (LCS). As a special case of the differential variational inequality (DVI), the LCS consists of a linear, time-invariant ODE and a linear complementarity problem. The extension to a nonlinear complementarity system (NCS) with analytic inputs turns out to be non-trivial as we need to use the Lie derivatives of analytic functions in order to arrive at an expansion of the solution trajectory near a given state. Further extension to a differential variational inequality is obtained via its equivalent Karush-Kuhn-Tucker formulation. For the second topic, which is classical in system theory, we use the non-Zenoness result and the recent results in a previous paper pertaining to the B-differentiability of the solution operator of a nonsmooth ODE to obtain a sufficient condition for the short-time local observability of a given strongly regular state of an NCS. Refined sufficient conditions and necessary conditions for local observability of the LCS satisfying the P-property are obtained     

Sensor location for discrete mode observability of switching linear systems with unknown inputs

This paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs. Such a property is quite important for designing control laws, observers, fault detection and isolation schemes (when the fault occurrence implies a commutation between two modes), and so on. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, new necessary and sufficient conditions for discrete mode generic observability. When these conditions are not satisfied, we propose a sensor placement procedure which allows us to recover the mode observability. Our approach can be implemented by classical and quite simple graph-theory algorithms.     

On the Reachability Problem for Uncertain Hybrid Systems

In this paper, we revisit the problem of designing controllers to meet safety specifications for hybrid systems, whose evolution is affected by both control and disturbance inputs. The problem is formulated as a dynamic game and an appropriate notion of hybrid strategy for the control inputs is developed. The design of hybrid strategies to meet safety specifications is based on an iteration of alternating discrete and continuous safety calculations. We show that, under certain assumptions, the iteration converges to a fixed point, which turns out to be the maximal set of states for which the safety specifications can be met. The continuous part of the calculation relies on the computation of the set of winning states for one player in a two player, two target, pursuit evasion differential game. We develop a characterization of these winning states (as well as the winning states for the other player for completeness) using methods from nonsmooth analysis and viability theory.