一类Markov跳跃非线性系统的鲁棒自适应镇定

研究一类具有Markov 跳跃参数的随机非线性系统的鲁棒自适应镇定问题.利用随机控制的Lyapunov 设计方法,对受Wiener 噪声干扰的参数严格反馈形式的跳跃系统,利用backstepping 方法设计参数自适应律和控制律,使得闭环系统状态在4 阶矩意义下全局一致有界,并能收敛到平衡点的任意小邻域内.仿真结果表明了该设计方法的有效性.     

具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

研究了一类随机非线性系统的逆最优增益设计问题,系统中除了方差未知的Wiener噪声之外,还含有Markov跳跃参数. 首先,给出此类系统逆最优增益设计问题可解的一个充分条件. 其次,针对一类具有严格反馈形式的随机非线性系统,利用积分反推法,给出了依概率全局渐近稳定和逆最优控制策略的设计方法. 其中,所设计的Lyapunov函数和控制策略与模态显式无关,克服了由于Markov跳跃模态引起的耦合项所带来的设计困难. 最后,通过仿真验证了控制策略的有效性.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

Passivity,Feedback Equivalence and Global Stabilization of Nonlinear Markovian Jump Systems

This paper combines the passivity theory with geometric control theory for nonlinear Markovian jump systems. The key point concentrates on taking the appropriate coordinate changes following with the Markovian switchings. Based on this concept, we investigate the passivity, feedback equivalence and global stabilization problems, which implies that under a proposed strongly minimum‐phase condition, the nonlinear Markovian jump system is feedback equivalent to a passive system. A numerical example is presented to illustrate the effectiveness of our results.     

Almost Sure Exponential Stabilization of a Class of Uncertain Stochastic Systems with Markovian Switching

This paper is concerned with the almost sure exponential stabilization of a class of uncertain stochastic systems with Markovian switching. A new criterion for testing the stability of such systems is established. The approach is based on stationary distribution theory. A sufficient condition is proposed for the design of robust state‐feedback controllers. An example illustrates the proposed techniques.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

Robust Stochastic Stability for a Class of Singular Systems with Uncertain Markovian Jump and Time‐Varying Delay

This paper deals with the problem of the robust stochastic stability for a class of singular systems with uncertain Markovian jump and time‐varying delay. Sufficient conditions on the stochastic stability are presented. The obtained results are formulated in terms of strict linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed approaches.     

广义马氏跳变系统在一般转移速率下的控制器设计

针对转移概率不能精确获得并且部分未知的广义马氏跳变系统, 分别讨论在模态依赖控制器和模态独立控制器条件下的系统镇定问题. 与现有结果相比, 所提研究方法具有较小的保守性, 能够有效地解决实际问题. 首先, 运用自由权矩阵方法, 得到了广义马氏跳变系统在转移速率满足上述一般条件时系统随机容许的充分条件. 在此基础上, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式分别给出了模态依赖和模态独立控制器的求解条件. 最后, 通过数值算例验证设计方法的有效性和优越性.     

Stabilization for Switched LPV Systems with Markovian Jump Parameters and Its Application

This paper is concerned with the stabilization problem for a class of switched linear parameter‐varying (LPV) systems with Markovian jump parameters whose transition rate is completely unknown, or only its estimated value is known. Firstly, a new criterion for testing the stochastic stability of such systems is established. Then, using the multiple parameter‐dependent Lyapunov function method, we design a parameter‐dependent state‐feedback controller for individual switched LPV subsystem to guarantee stochastic stability of the closed‐loop switched LPV systems with Markovian jump parameters under uncertain transition rates. Finally, as an application of the proposed design method, the stabilization problem of a turbofan‐engine which cannot be handled by the existing methods is investigated.     

Markovian跳变不确定分布参数系统随机稳定性分析

研究了一类具有Markovian跳变的不确定分布参数系统的随机稳定性问题。基于线性矩阵不等式方法,通过构造适当的随机Lyapunov泛函,计算弱无穷小算子,利用Green公式及Schur补引理,系统随机稳定的充分条件以一组线性矩阵不等式给出。线性矩阵不等式很容易通过MATLAB中的LMI工具箱进行求解。该充分条件便于工程实际应用。最后,构建仿真模型验证了该方法的有效性。     

一类虚拟控制系数未知的随机非线性时滞大系统的适应镇定控制

研究了一类具有未知虚拟控制系数和未知噪声协方差的随机非线性时滞大系统的适应镇定问题. 首先, 针对系统的未知虚拟控制系数和未知噪声协方差, 选取了相应的估计参数; 然后, 针对时变时滞对闭环系统稳定性的影响, 构造了适当形式的Lyapunov-Krasovskii泛函, 采用积分反推方法给出了无记忆状态反馈控制律的系统设计过程. 在一定条件下, 证明了闭环系统平衡点依概率全局稳定, 且除参数估计以外的所有闭环信号几乎均收敛到零点. 仿真算例验证了所给方法的有效性.     

State Feedback Control for Discrete‐time Markovian Jump Systems with Random Communication Time Delay

This paper concerns the stabilization problem for a class of networked control system with Markovian parameter using mode dependent state feed‐back controller through a wireless networked control system. The problem that the random network‐induced delays generated both by wireless connection contention and the movement of wireless nodes is taken into consideration. The mode dependent controller can be obtained by solving a set of parameterized bilinear matrix inequalities (BMIs). A numerical example is exhibited to show the effectiveness of the proposed design method.     

不确定非线性系统的鲁棒输出反馈自适应控制

针对一类具有一般不确定性的非线性系统,设计一种新的鲁棒输出反馈自适应控制器。在较弱条件下,该控制器不仅能保证闭环系统全局稳定,且能使跟踪误差以指数速度收敛到零的小领域内。仿真结果验证了所给控制方案的有效性。     

Probability Analysis of Terminal Sliding Mode Control of Second‐Order Markovian Jump Systems

This paper explores the probability problems on terminal sliding mode control of second‐order nonlinear continuous Markovian jump systems. An equivalent control based terminal sliding mode control scheme is proposed that can guarantee the systems' finite time mean‐square stability. By introducing a multi‐step transition conditional probability, the novel reaching and sliding probabilities are derived for the situations where the control force is not strong enough. This indicates that the reaching and sliding probabilities are both monotonically bounded non‐decreasing non‐negative piecewise right‐continuous functions of the control parameter. A numerical example is given to show the feasibility of the theoretical results.     

随机非线性严格反馈系统的自适应神经网络输出反馈镇定

针对具有严格反馈形式的随机非线性系统, 首次引入神经网络控制技术, 设计了适当形式的随机控制 Lyapunov函数, 并运用反推(Backstepping)技术和非线性观测器设计技术, 构造出一类自适应神经网络输出反馈控制器. 在一定条件下, 证明了闭环系统平衡点依概率稳定. 仿真算例验证了所给控制方案的有效性.     

具有马氏跳跃参数的切削加工系统控制问题研究

以单刀具垂直切削加工系统为研究对象, 引入了变进给量控制方法, 建立了具有Markov跳跃参数的时变时滞跳跃系统模型. 通过对系统的随机稳定性分析, 给出了使系统呈均方意义下指数稳定的充分条件, 同时研究了在系统参数矩阵和状态转移率非精确可知情形下的鲁棒稳定性条件, 并讨论了时变时滞参数对系统状态变量指数衰减速率的影响关系. 最后以仿真算例说明了本文所提方案的有效性.     

Reliable Dissipative Control for a Class of Uncertain Singular Markovian Jump Systems via Hybrid Impulsive Control

In this paper, the problem of robust normalization and reliable dissipative control is investigated for a class of uncertain singular Markovian jump systems with actuator failures. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional–derivative control strategy is presented. The gain matrices of the impulsive control part can be obtained together with the design approach. Moreover, the dissipative control results obtained in this paper include the results of H‐infinity and passive control as special cases. Finally, two numerical examples are provided to illustrate the effectiveness and applicability of the proposed methods.     

含参数不确定性的马尔可夫跳变过程鲁棒正实控制

讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.     

Distributed Control Design for Spatially Interconnected Markovian Jump Systems With Time‐Varying Delays

This paper focuses on spatially interconnected Markovian jump systems with time‐varying delays. Firstly, a sufficient condition is given to check the well‐posedness, stochastic stability and contractiveness of spatially interconnected systems with the effect of time‐varying delays and Markovian jumping parameters. Secondly, the distributed controllers which inherit the structure of the plants are designed. A sufficient and necessary condition is proposed to guarantee the existence of the distributed controllers. Finally, an illustrative numerical example is given to show the effectiveness of the results.     

一类非线性随机系统的自适应控制

本文在文献「１，２」的基础上，对一类仿射非线性随机系统的最小二乘（ＬＳ）自适应控制问题进行了分析，给出了稳定性及收敛速度结果，在这里，我们仅要求非线性函数具有线性增长速度，而无需任何其它结构假设。