模态跳变概率可控的Markov跳变线性系统的优化

研究模态跳变概率可控的Markov跣变线性二次模型的最优控制问题,考虑两类模态跳变控制策略:开环模态控制和闭环模态控制,应用策略迭代和性能势的概念,给出了最优的闭环模态控制优于最优的开环模态控制的充分条件,以指导最优控制器的设计,在已知最优的开环模态控制策略的基础上,应用策略迭代给出了构造闭环模态控制策略的方法,以进一步改善系统的性能.     

随机激励的非线性Markov跳变系统的稳态响应

大量实际工程问题需要用同时包含连续和离散变量的Markov跳变系统来描述.本文介绍了一类随机激励的单自由度(强)非线性Markov跳变系统的稳态响应的研究方法.首先,基于随机平均法导出具有Markov跳变参数的平均It随机微分方程,原系统方程的维数得到降低.接着,根据跳变过程原理,建立Fokker-Planck-Kolmogorov(FPK)方程组,方程组中的方程与系统的结构状态一一对应且互相耦合.求解该FPK方程组,得到Markov跳变系统的稳态随机响应及其统计量.最后,以一个高斯白噪声激励的Markov跳变Duffing振子为例,计算得到不同跳变规律下系统的稳态响应.研究结果表明,Markov跳变系统的稳态响应可以看作是各结构状态子系统稳态响应的加权和,加权值由跳变规律决定.     

一类连续广义Markov跳变系统的镇定性研究

研究转移概率部分未知情况下的连续时间广义Markov跳变系统的稳定性和镇定性.所研究的系统涵盖了转移概率完全已知和完全未知两种特殊情况,具有更广泛的意义.首先,基于线性矩阵不等式方法,获得了使系统正则、无脉冲、随机稳定的充分条件;然后,设计了基于线性矩阵不等式条件的状态反馈控制器,使闭环系统正则、无脉冲、随机稳定;最后,通过仿真算例验证了所提出方法的有效性.     

一类不确定离散Markov 跳变系统滑模状态反馈控制

针对具有不确定的离散Markov跳变系统,研究其滑模状态反馈控制问题.考虑系统的不确定满足匹配条件,以线性矩阵不等式形式给出了离散滑模面存在的充分条件,设计了具有指数趋近律的滑模控制器,保证了系统状态到达滑模面并在滑模带上随机镇定.数值仿真验证了所提出的控制方案的有效性.     

模型不确定非线性Markov 跳变系统的滤波算法

针对模型不确定非线性Markov跳变系统,提出一种新的滤波算法.相比于传统交互多模型粒子滤波,该方法通过引入前一时刻的滤波误差来增强原先由于不精确模型而造成权值较小的真实粒子在滤波过程中的作用,以此来改善算法的估计性能.仿真结果表明,该方法在处理含不确定模型参数的非线性Markov跳变系统状态估计问题时具有较好的性能.     

一类双向确定性系统最优控制问题的最大值原理

本文讨论了一类双向确定性系统的最优控制问题，我们利用Ｅｋｅｌａｎｄ变分原理，推得了最优控制所满足的最大原理。同时，对线性系统的情况，我们还证明了最大值条件的充分性。     

一类Markov跳变系统的综合时频分析模型切换检测

在Markov跳变系统的估计问题中,目前的多模型估计器采用模型概率检测模型切换;这是一种基于信号幅值的检测方法;事实上,模型切换表征了系统的暂态过程,因而系统某些特征的频谱特性在模型切换前后存在差异;因此提出一类Markov跳变系统的综合时频分析模型切换检测方案（ITFA）;同时给出统计意义下的模型检测评价指标;仿真结果表明：与标准的交互式多模型算法相比,ITFA方法具有检测概率高、延迟时间小的优点;同时,ITFA对于先验性的滑窗长度、检测阈值具有较好的鲁棒性.     

Markov跳变系统的非同步事件触发耗散容错控制

本文主要研究一类具有执行器故障的Markov跳变系统的非同步事件触发耗散容错控制问题.通过引入非同步事件触发器来降低传感器的采样数据传输频率,从而降低通信消耗.采用两个独立的隐Markov模型分别描述触发器、控制器与原系统之间的非同步现象.在此框架下,基于Lyapunov稳定性和耗散理论,得到了闭环控制系统在执行器存在故障的情况下随机稳定并严格耗散的充分条件.并借助矩阵不等式变换技术给出了触发器和控制器矩阵参数的求解方法,实现了触发器和控制器的协同设计.最后,通过仿真研究验证了所提出的设计方法的有效性.     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

Robust control of continuous-time Markov jump linear systems

This paper is concerned with the problem of designing robust H₂ state-feedback controllers for continuous-time Markov jump linear systems subject to polytopic-type parameter uncertainty. Based on the parameter-dependent Lyapunov function approach, a new method for designing robust H₂ controllers is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed design method.     

Quantized feedback stabilization of continuous-time Markov jump systems under asynchronous control

This paper addresses a new asynchronous control scheme for continuous-time Markov jump linear systems (MJLSs). Both controlled system and quantizer are asynchronous with the controller due to the process by which the controller can accurately observe and emit the switching signal being stochastic. The random variable satisfying Bernoulli distribution is introduced to describe this observation. On this basis, two methods are proposed to obtain sufficient conditions for exponential almost sure stability and almost surely asymptotically stability, respectively from the perspective of the linear matrix inequality (LMI). The results are independent of the asynchronous time interval. Finally, a numerical example demonstrates the validity and feasibility of developed theoretical results.     

基于策略迭代算法的连续时间线性Markov跳变系统非零和微分反馈Nash控制

针对一类连续时间线性Markov跳变系统,本文提出了一种新的策略迭代算法用于求解系统的非零和微分反馈Nash控制问题.通过求解耦合的数值迭代解,以获得具有线性动力学特性和无限时域二次成本的双层非零和微分策略的Nash均衡解.在每一个策略层,采用策略迭代算法来计算与每一组给定的反馈控制策略相关联的最小无限时域值函数.然后,通过子系统分解将Markov跳变系统分解为N个并行的子系统,并将该算法应用于跳变系统.本文提出的策略迭代算法可以很容易求解非零和微分策略所对应的耦合代数Riccati方程,且对高维系统有效.最后通过仿真示例证明了本文设计方法的有效性和可行性.     

Robust M-ary detection filters and smoothers for continuous-time jump Markov systems

In this paper, we consider a dynamic M-ary detection problem when Markov chains are observed through a Wiener process. These systems are fully specified by a candidate set of parameters, whose elements are, a rate matrix for the Markov chain and a parameter for the observation model. Further, we suppose these parameter sets can switch according to the state of an unobserved Markov chain and thereby produce an observation process generated by time varying (jump stochastic) parameter sets. Given such an observation process and a specified collection of models, we estimate the probabilities of each model parameter set explaining the observation. By defining a new augmented state process, then applying the method of reference probability, we compute matrix-valued dynamics, whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process. These matrix-valued dynamics satisfy a stochastic integral equation with a Wiener process integrator. Using the gauge transformation techniques introduced by Clark and a pointwise matrix product, we compute robust matrix-valued dynamics for the joint probabilities on the augmented state space. In these new dynamics, the observation Wiener process appears as a parameter matrix in a linear ordinary differential equation, rather than an integrator in a stochastic integral equation. It is shown that these robust dynamics, when discretised, enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path. In contrast, no such upper bounds can be computed for Taylor expansion approximations, such as the Euler-Maryauana and Milstein schemes. Finally, by exploiting a duality between causal and anticausal robust detector dynamics, we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations. A computer simulation demonstrating performance is included.     

Optimal fault-tolerant control for Markov jump power systems with asynchronous actuator faults

Communication problems in the sensor-to-controller and controller-to-actuator channels can cause both the controller and actuator to run asynchronously with the original system in different operating modes. This paper investigates an optimal fault-tolerant control approach for Markov jump power systems (MJPSs) with asynchronous controller and actuator. Firstly, an asynchronous controller is proposed to deal with incomplete information (i.e., system modes) transmission in the sensor-to-controller channel. Secondly, a new asynchronous actuator faults model is constructed to simultaneously represent the two partial losses, of modes information in the controller-to-actuator channel, and of control effectiveness (LoCE) caused by actuator faults. Under this framework, two related hidden Markov models (HMMs) are formed, which reveal that both the controller and actuator are asynchronous with the controlled system in different modes. By using Lyapunov and optimal approaches, sufficient conditions are derived to ensure that MJPSs are mean square stable with an optimal guaranteed cost. Finally, Monte Carlo simulations are used to verify the effectiveness of the proposed control method.     

Optimal linear mean square filter for continuous-time jump linear systems

We consider a class of hybrid systems which is modeled by continuous-time linear systems with Markovian jumps in the parameters (LSMJP). Our aim is to derive the best linear mean square estimator for such systems. The approach adopted here produces a filter which bears those desirable properties of the Kalman filter: A recursive scheme suitable for computer implementation which allows some offline computation that alleviates the computational burden. Apart from the intrinsic theoretical interest of the problem in its own right and the application-oriented motivation of getting more easily implementable filters, another compelling reason why the study here is pertinent has to do with the fact that the optimal nonlinear filter for our estimation problem is not computable via a finite computation (the filter is infinite dimensional). Our filter has dimension Nn, with n denoting the dimension of the state vector and N the number of states of the Markov chain.     

Switching predictive control for continuous-time Markovian jump delay systems

This paper is concerned with switching model predictive control (SMPC) for continuous-time Markovian jump delay systems (MJDSs). First, a piecewise constant switching predictive controller, which only depends on the average dwell time (ADT) switching laws rather than the jumping modes, is obtained by employing the ADT approach under the infinite-time predictive control design framework. Such a control strategy is proposed to make a trade-off between robustness and adaptivity when the design complexity of mode-independent and mode-dependent MPC is considered. It is revealed that the SMPC can deal with MJDSs with both time varying and time invariant jump rates and cover the mode-independent MPC as a special cease. Second, the feasibility of the SMPC scheme and the mean square stability of the closed-loop MJDS are discussed by using the stochastic invariance of the ellipsoid set over each sampling period. A numerical example is given to illustrate the main results.     

On almost sure stability of continuous-time Markov jump linear systems

In this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out.     

H∞ control of continuous-time Markov jump linear systems with detector-based mode information†

This paper features new results on H_∞ analysis and control of linear systems with Markov jump disturbances, in a scenario of partial observations of the jump process. We consider the situations in which the jump process can only be measured through a suitable detector. A distinctive feature of the approach here is that it is general enough to encompass particular scenarios such as that of perfect information, no information (mode independent) and cluster observations of the Markov jump process. The main results, comprising a new bounded real lemma and a condition for state feedback synthesis, are expressed via linear matrix inequality-based optimisation problems. The method devised for the design of H_∞ controllers is applied to the control of an unmanned aerial vehicle model.     

Optimal semistable control for continuous-time linear systems

In this paper, we develop a new H₂ semistability theory for linear dynamical systems. Specifically, necessary and sufficient conditions based on the new notion of weak semiobservability for the existence of solutions to the semistable Lyapunov equation are derived. Unlike the standard H₂ optimal control problem, a complicating feature of the H₂ optimal semistable control problem is that the semistable Lyapunov equation can admit multiple solutions. We characterize all the solutions using matrix analysis tools. With this theory, we present a new framework to design H₂ optimal semistable controllers for linear coupled systems by converting the original optimal control problem into a convex optimization problem.