Stability of digital control systems implemented in error-recoverable computers

Safety-critical, real-time applications make use of fault-tolerant digital control systems to achieve their performance goals. Even though these digital control systems are fault-tolerant, they are susceptible to errors induced by common-mode faults, since these errors cannot be masked by standard redundancy provisions. Such errors can be handled by special error correction mechanisms, which could require stopping the control law computations while the errors are removed. Thus, the effect of these special error recovery mechanisms on digital control systems needs to be understood. This paper presents a comprehensive study of the effect of three error recovery mechanisms–rollback, reset and cold restart–on the stability of digital closed-loop control systems. The effect of the faults, detected and handled by these error recovery mechanisms, on the digital control system is modelled by a set of interference maps. It is assumed that the arrival and departure of common-mode faults can be represented by a Markov process. The overall system behaviour is then described by a Markov jump linear model, whose stability is explored using standard techniques from the literature. The result of this analysis is a new metric, the minimum average interarrival spacing (MAIS), which is useful for comparing the performance of different error recovery mechanisms and for designing new fault-tolerant controllers. The theoretical results are illustrated via Monte Carlo simulations that show the effects of common-mode faults on the closed-loop stability of the longitudinal dynamics of an AFTI/F-16 aircraft.     

线性Markov跳变随机系统的Pareto最优控制

目前针对多个主体、多个目标的带有Markov跳变的线性随机系统的控制问题的研究较少且较为浅显.本文研究了具有乘性噪声的连续时间线性Markov跳变随机系统的Pareto最优控制问题.假设多个主体、多个性能指标由状态和控制变量中的二次部分和线性部分的线性组合而形成,证明了Pareto最优与加权和优化之间的关系,从而将多目标优化问题转化为特殊的单目标加权和最优控制问题.基于Pareto博弈理论与广义It?o公式,系统的Pareto有效策略可以通过一组耦合的广义Riccati微分方程与一组耦合的线性微分方程求解,并且可以得到每一个控制器的Pareto解.最后,本文通过数值仿真验证理论结果的有效性.     

Adaptive event-triggered robust H∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time-varying delay

This paper considers an adaptive event-triggered robust H_∞ control for the Takagi–Sugeno (T-S) fuzzy under the networked Markov jump systems (NMJSs) with time-varying delay. First, a new adaptive event-triggered scheme is developed to guarantee the T-S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state-feedback controller (mode-dependent) in a closed-loop form for stochastic stability for all admissible parameter uncertainties with an H_∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck-trailer application is used to demonstrate the effectively of the proposed algorithms.     

具有乘性噪声的线性离散时间随机控制系统综述

具有乘性噪声的随机不确定系统的控制问题有着广泛的应用背景. 本文概述了具有乘性噪声的线性离散时间随机系统的稳定性分析、均方镇定、最优控制以及最优估计问题和相关结论. 同时, 本文研究了具有状态与控制乘性噪声的线性多变量离散时间系统的均方镇定和最优控制问题, 分析了这两个问题之间的联系, 并讨论了最优状态反馈控制器的设计算法.     

Digital computer manipulation of high-order linear system equations including systems with input derivatives†

A systematic method for the digital computer manipulation of the equations describing high-order linear processes into canonic state space form is briefly reviewed. The basic method is then extended to embrace system models which, it transpires, include input derivative terms. The paper concludes with a numerical example relating to a boiler dynamic model described by a set of 23 differential and algebraic equations. This example, in addition to illustrating the method of equation manipulation proposed brings out, quite simply, certain features of the boiler model in question which have not been discussed in previous papers.     

具有双边随机时延和丢包的网络控制系统有限时间控制

针对双边丢包和双边时延的网络化控制系统的有限时间控制问题,通过引入时间偏移量的方法,将丢包转换为时延,从而形成多时延系统,并将时间延迟转换为系统状态延迟。基于全概率公式给出已知网络丢包率下连续丢包的概率公式,用Markov链表征网络时延的变化规律。以线性矩阵不等式的形式给出改进的有限时间时延相关稳定性判据,并通过数值仿真验证所提方法的有效性。     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

随机马尔可夫跳变系统的变结构控制设计

采用滑动扇区方法,研究了不确定随机马尔可夫跳变系统的变结构控制设计问题。首先给出随机马尔可夫跳变系统滑动扇区的定义,然后基于线性矩阵不等式技术,提出一种滑动扇区及变结构控制律设计方法。经过理论证明该控制律能够确保随机马尔可夫跳变不确定系统二次稳定,并有效地抑制抖振。最后数值仿真算例验证了控制方案的有效性。     

随机时滞马尔可夫跳跃系统的比例–积分跟踪控制

针对具有时变时滞和未知非线性的随机马尔可夫跳变系统,基于传统的PI控制策略和线性矩阵不等式算法,提出一种具有随机稳定性能、跟踪性能和鲁棒性能的多目标控制器设计方案.运用Lyapunov稳定性理论并引入L<,1>性能指标,构造出具有PI结构的跟踪控制器,保证了随机马尔可大跳跃系统的稳定性和跟踪性能,实现了系统跟踪性能的优...     

带有乘性过程噪声和模式观测时滞离散马氏跳线性系统的状态估计

研究受乘性过程噪声干扰的离散马氏跳线性系统状态估计问题. 系统可得到的观测包括两部分: 模式观测和输出观测, 其中模式观测受到固定时滞的影响. 利用贝叶斯定理及所得到的一些结果, 提出一种新颖的最小均方误差意义下次优状态估计算法. 该次优算法是回归的, 并且不随着时间增加而加重计算存储负荷. 通过计算机仿真来评估所提出次优算法的性能, 仿真结果验证了该算法的优越性.

     

Predictor Feedback Stabilization of Stochastic Linear Delayed Systems with Both Additive and Multiplicative Noises

In this paper we investigate memory control of stochastic linear delayed systems with both additive and multiplicative noises. A new formula is first presented to obtain the prediction vector from the system dynamics and then it is used for feedback to reduce the input delay in the original delayed system. To ensure the stability of closed‐loop system, some matrix inequality conditions are given that in the case of feasibility provide the stabilizing gain of the predictor controller. The proposed method is applied to stochastic quarter‐car model of an active suspension system to show the effectiveness of the approach.     

推广形式传输控制协议流量控制方程的方差稳定性

给定计算机网络中的传输控制协议（transmission control protocol,TCP）流量控制算法,如何确定其稳定域,是网络设计中的一个重要问题.由于网络上控制算法受大量随机因素影响,这相当于对一个由随机微分/差分方程描述的控制系统进行稳定性分析.目前已有研究大多直接对系统方程取期望,转为讨论期望的稳定性,而简单忽略受控TCP流的随机震荡.本文意在指出这种随机震荡给稳定性带来的不可忽视的影响.本文以TCP/RED（含早期随机检测的TCP流）系统为例,首先,从系统的随机微分方程出发,通过在平衡点处线性化,将系统化为含加乘混合噪声的多维线性时不变系统.然后,给出了分别对应时间连续与离散情况的推广的TCP流量控制方程,即含多噪声源的一次时不变随机微分/差分方程组.接着,对此推广形式,推导了其协方差矩阵所满足的矩阵方程,并在此基础上,得到了协方差矩阵极限渐近稳定的充要条件以及此极限的计算公式.在工程设计中,此条件可以作为系统稳定与否的一个替代判据,方差极限公式可用来估计系统的运动范围.最后,将一般公式应用到具体例子上,展示了考虑方差稳定性后系统稳定域的变化.进一步,仿照确定性系统中的处理方法,本文结论还可推广到非线性系统及时变系统.