网络控制系统的稳定性分析

在网络控制系统中,由于网络的通讯带宽的限制、信息(包括传感器信号,控制器信号,等等)的碰撞等诸多原因,不可避免地会使信息在传输过程中存在时延,称之为网络诱导时延.网络诱导时延是导致控制系统的性能降低,甚至使得系统不稳定的主要因素.为了克服网络诱导时延对控制系统造成的影响,建立了具有参数不确定性的线性网络控制系统模型,利用Razumikhin和Laypunov定理来估计传输时延的最大界,给出了网络控制系统渐进稳定的充分条件.并且由LMI方程给出了稳定的控制器增益K.仿真实例证明了结论的有效性.     

带马尔科夫跳和乘积噪声的随机系统的最优控制

讨论了N个选手随机系统的最优控制问题. 设计了无限时间的带有马尔科夫跳和乘积噪声的随机系统的Pareto最优控制器. 应用推广的Lyapunov方法和解随机Riccati代数方程得到了系统的Pareto最优解, 证明了最优控制器是稳定的反馈控制器, 以及对应于最优控制器的反馈增益中的随机Riccati代数方程的解是最小解.     

具有随机丢包的线性网络控制系统控制器设计

研究一类双向通道里同时存在随机数据包丢失的线性网络控制系统的控制器设计问题,随机数据包丢失同时存在于传感器-控制器和控制器-执行器网络通道里,随机数据包丢失采用满足Bernoulli分布的二进制切换序列来描述.在发生随机数据包丢失时,可采用闭环系统均方指数稳定的动态输出反馈控制器存在的充分性判据,并给出了基于线性矩阵不等式(LMI)的控制器求解方法,并通过一个仿真算例验证了控制器的正确性.     

δ算子下的网络控制系统最优控制方法

研究网络控制系统的随机最优控制问题，提出了针对随机时延的网络控制系统最优控制律和二次型性能指标极小的控制律设计方案．在δ算子域内应用动态规划理论．设计网络控制系统的最优状态反馈和输出反馈控制律，得到的线性二次型高斯控制器可对系统中的随机长时延进行动态补偿．最后通过实例仿真验证了上述最优控制方案的可行性和有效性．     

状态时滞的网络控制系统的保成本控制器设计

针对一类含状态时滞的网络控制系统，本文对此进行了状态反馈保成本控制器设计.在考虑网络引起的滞后的基础上，一个新的模型提出来了.保成本控制器的存在性也通过一系列线形矩阵不等式表达出来.一个能把非凸问题转换成凸问题的方法同时应用了.与此同时，相应的能获取最低性能指标的算法也已给出.配套的仿真例子证明了此算法的有效性.     

随机网络中的H∞输出跟踪控制研究

研究随机网络控制系统的输出跟踪问题。采用线性矩阵不等式方法,推导控制器存在的充分条件,介绍控制器的设计方法。该控制器能够保证相对于所有能量有界的外界扰动信号,随机网络控制系统的H∞性能指标小于一个定值γ。仿真实验结果表明,利用该方法设计的控制器输出误差较小。     

随机不确定网络控制系统的L_2-L_∞输出跟踪控制

本文研究了一类具有时延和凸多面体不确定性的随机网络控制系统的模型参考输出跟踪问题。基于线性矩阵不等式方法推出了该随机网络控制系统的稳定性和控制器设计的充分条件,并将控制器的设计转化为一个凸优化的求解问题。所设计的控制器能够保证相对于所有能量有界的外界扰动信号,随机网络控制系统的L2-L∞性能指标小于一定值γ。仿真实例证实了该设计方法的有效性。     

控制能量约束条件下时滞系统最优控制与仿真

文中对时滞系统在控制能量存在约束时的最优控制问题进行了探讨.由控制器Youla参数化得到控制系统的敏感度函数和控制敏感度函数用来表示一个包含跟踪误差和控制能量在内的积分平方性能指标,针对不同类型的时滞过程运用谱分解的方法最小化该性能指标,从而导出相应控制器的设计方法,可使系统在控制能量约束条件下具有最优的控制性能.仿真研究进一步说明了所给设计方法的有效性.     

基于脉冲切换控制的网络控制系统的镇定性

在网络控制系统的优化中,研究了离散时间域内带随机时延的网络控制系统的镇定性优化问题.首先将随机时延建模为一个马尔可夫链,然后在网络控制系统中引入模态依赖的脉冲切换控制器,建立了采用脉冲切换控制的网络控制系统模型.利用系统模型随机稳定性理论推导,得到使网络控制系统稳定的充分必要条件,并用迭代线性矩阵不等式方法求解了控制器,最后利用小车倒立摆做被控对象进行了数值仿真,仿真结果说明了控制方法的有效性.     

事件驱动的网络化系统最优控制

针对随机事件驱动的网络化控制系统, 研究其中的有限时域和无限时域内最优控制器的设计问题. 首先, 根据执行器介质访问机制将网络化控制系统建模为具有多个状态的马尔科夫跳变系统; 然后, 基于动态规划和马尔科夫跳变线性系统理论设计满足二次型性能指标的最优控制序列, 通过求解耦合黎卡提方程的镇定解, 给出最优控制律的计算方法, 使得网络化控制系统均方指数稳定; 最后, 通过仿真实验表明了所提出方法的有效性.

     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear stochastic receding horizon control: stability,robustness and Monte Carlo methods for control approximation

This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors. In each case, it is shown that the controller approximation errors do not accumulate (even over an infinite time frame) and the process converges exponentially fast to a small neighbourhood of the origin. In addition to this analysis, an approximation method for receding horizon optimal control is proposed based on Monte Carlo simulation. This method is derived via the Feynman–Kac formula which gives a stochastic interpretation for the solution of a Hamilton–Jacobi–Bellman equation associated with the true optimal controller. It is shown, and it is a prime motivation for this study, that this particular controller approximation method practically stabilises the underlying nonlinear process.     

Predictive control for networked systems affected by correlated packet loss

In this paper, we consider the predictive control problem of designing receding horizon controllers for networked linear systems subject to random packet loss in the controller to actuator link. The packet dropouts are temporarily correlated in the sense that they obey a Markovian transition model. Our design task is to solve the optimal controller that minimizes a given receding horizon cost function, using the available packet loss history. Due to the correlated nature of the packet loss, standard linear quadratic regulator methods do not apply. We first present the optimal control law by considering the correlations. This controller turns out to depend on the packet loss history and would typically require a large lookup table for implementation when the Markovian order is high. To address this issue, we present and compare several suboptimal design approaches to reduce the number of control laws.     

具有瑞利平坦衰落信道的线性系统线性二次高斯控制

网络化控制系统中的通信约束问题一直是人们关注的焦点. 本文讨论了具有信号衰落约束的线性系统的线性二次高斯(LQG)控制问题, 其中系统输出经放大后通过瑞利平坦衰落信道传输到控制器. 针对控制器与通信信号放大设计的折中问题, 本文在系统二次型性能指标中进一步考虑通信过程的能量消耗, 并基于离线设计放大系数, 给出了有限时域下控制信号与放大系数的设计方法. 对于线性定常系统, 采用本文方法设计得到的放大系数在时间趋于无穷时将为常数, 基于此, 本文进一步将方法推广到无限时域情形. 仿真结果说明了本文方法的有效性及其性能.     

Robust output feedback stabilization via risk-sensitive control

We consider a problem of robust linear quadratic Gaussian (LQG) control for discrete-time stochastic uncertain systems with partial state measurements. For a finite-horizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398). In this paper, an infinite horizon extension of the results of Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398) is discussed. We show that for a broad class of uncertain systems under consideration, a controller constructed in terms of the solution to a specially parameterized risk-sensitive stochastic control problem absolutely stabilizes the stochastic uncertain system.     

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

In this paper, the stochastic optimal control of linear networked control system (NCS) with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived. The proposed stochastic optimal control method uses an adaptive estimator (AE) and ideas from Q-learning to solve the infinite horizon optimal regulation of unknown NCS with time-varying system matrices. Next, a stochastic suboptimal control scheme which uses AE and Q-learning is introduced for the regulation of unknown linear time-invariant NCS that is derived using certainty equivalence property. Update laws for online tuning the unknown parameters of the AE to obtain the Q-function are derived. Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control signals converge to optimal or suboptimal control inputs. Simulation results are included to show the effectiveness of the proposed schemes. The result is an optimal control scheme that operates forward-in-time manner for unknown linear systems in contrast with standard Riccati equation-based schemes which function backward-in-time.     

Stochastic differential games and inverse optimal control and stopper policies

In this paper, we consider a two-player stochastic differential game problem over an infinite time horizon where the players invoke controller and stopper strategies on a nonlinear stochastic differential game problem driven by Brownian motion. The optimal strategies for the two players are given explicitly by exploiting connections between stochastic Lyapunov stability theory and stochastic Hamilton–Jacobi–Isaacs theory. In particular, we show that asymptotic stability in probability of the differential game problem is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Isaacs equation, and hence, guaranteeing both stochastic stability and optimality of the closed-loop control and stopper policies. In addition, we develop optimal feedback controller and stopper policies for affine nonlinear systems using an inverse optimality framework tailored to the stochastic differential game problem. These results are then used to provide extensions of the linear feedback controller and stopper policies obtained in the literature to nonlinear feedback controllers and stoppers that minimise and maximise general polynomial and multilinear performance criteria.     

线性时序逻辑约束下的滚动时域控制路径规划

针对有限确定性系统中的路径规划问题,本文提出了一种线性时序逻辑约束下的在线实时求解滚动时域控制的新方法。该方法将滚动时域控制方法和满足线性时序逻辑公式的策略相结合,控制目标是在满足高级别任务规范的同时,使收集的累积回报值最大化。其中,在有限时域内的每个时间步长上局部优化回报值,并应用当前时刻计算获得的最优控制序列。通过执行适当的约束,保证控制器产生的无限轨迹满足期望的时序逻辑公式。而且,由于地势影响因子的引入,所建议的方案更接近于真实情况。仿真实验结果验证了文中提出方法的可行性和有效性。     

线性Markov 切换系统的随机Nash 微分博弈及混合H2/H∞ 控制

研究线性Markov切换系统的随机Nash微分博弈问题。首先借助线性Markov切换系统随机最优控制的相关结果,得到了有限时域和无线时域Nash均衡解的存在条件等价于其相应微分(代数) Riccati方程存在解,并给出了最优解的显式形式;然后应用相应的微分博弈结果分析线性Markov切换系统的混合H2/H∞控制问题;最后通过数值算例验证了所提出方法的可行性。