严格反馈随机非线性系统风险灵敏度输出反馈控制器设计

研究了一类严格反馈随机非线性系统的输出反馈设计问题.在无限时区风险灵敏度指标下,应用积分反推(integrator backstepping)技术,设计了控制器.所设计的控制器能够保障对任意风险灵敏度系数具有任意小的指标,并且闭环系统为概率意义下有界的.特别地,所设计的控制器还能保证控制器的平衡条件.仿真例子验证了理论结果的正确性.     

Markov跳跃非线性系统逆最优增益设计

证明了一类严格反馈Markov跳跃系统是依概率输入–状态可稳定的.其次,证明了逆最优增益设计问题可解的一个充分条件是存在一组满足小控制量的依概率输入–状态稳定控制李雅普诺夫函数.最后,利用积分反推方法,给出了严格反馈Markov跳跃系统逆最优增益设计问题的一个构造性解.其中,为了克服由于Markov跳跃引起的耦合项所带来的困难,所设计的李雅普诺夫函数以及控制器是与模态无关的.     

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.     

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.     

离散随机Markov跳跃系统有限时间有界控制

研究一类带乘性噪声的离散时间随机Markov跳跃系统的有限时间控制问题.首先,定义系统的有限时间稳定和有限时间有界,通过逐次迭代和条件期望给出系统有限时间稳定的充分必要条件;其次,针对含干扰的系统,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间有界的充分条件并设计状态反馈镇定控制器;然后,进一步考虑转移概率信息不完全下的有限时间有界问题;最后,通过数值例子验证了所提出方法的有效性.     

基于S类函数的严格反馈非线性周期系统的自适应控制

针对一类严格反馈非线性周期系统, 在周期非线性可时变参数化的条件下设计自适应控制器. 通过将周期时变参数展开成傅里叶级数, 并采用微分自适应律估计未知系数, 进行控制器反推设计. 引入S类函数, 并在控制器设计中应用S类函数处理截断误差项对系统跟踪性能的影响, 同时, S类函数能确保虚拟控制的可微. 给出几种不同的S类函数设计, 分析比较将其应用于控制器设计时产生的不同效果. 理论分析与仿真结果表明, 提出的控制方法能够实现系统输出跟踪期望轨迹, 且闭环系统所有信号有界.     

严格反馈非线性时变系统的迭代学习控制

针对一类含未知时变参数的严格反馈非线性系统, 提出一种实现有限作业区间轨迹跟踪控制的迭代学习算法. 基于Lyapunov-like方法设计控制器, 回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求. 以反推设计(Backstepping)方法设计控制器, 为使得虚拟控制项可导, 引入一级数收敛序列; 将时变参数展开为有限项多项式形式, 在控制器设计中采取双曲正切函数处理余项对于系统跟踪性能的影响. 理论分析表明, 闭环系统所有信号有界, 并能够实现系统输出完全收敛于理想轨迹.     

奇异Markov跳跃系统的鲁棒故障检测

研究受L2有界未知输入影响的一类奇异Markov跳跃系统的鲁棒故障检测问题。采用基于观测器的故障检测滤波器（FDF）作为残差产生器,将故障检测滤波器的设计归结为随机意义下的H∞滤波问题。推导并证明了问题可解的充分条件,并通过求解线性矩阵不等式得到了故障检测滤波器参数矩阵的解。算例验证了所给算法的有效性。     

一类纯反馈非线性系统的动态面控制

针对一类非仿射输入纯反馈非线性系统,提出了一种动态面控制算法.不同于运用中值定理,该算法通过引入一个辅助系统,将原系统转化为输入仿射系统,结合动态面控制与反推设计法,消除了反推法中"计算膨胀"问题.所设计控制器保证了闭环系统所有信号半全局一致最终有界,且通过选择合适的设计参数可使跟踪误差收敛到原点的一个小邻域内.一个仿真实例进一步验证了所提控制算法的有效性.     

确保估计性能的离散Markov跳跃系统鲁棒Kalman滤波

本文研究一类具有不确定噪声的离散时fnqMarkov跳跃线性系统的鲁棒Kalman滤波器设计问题.文中基于确保状态估计误差性能指标的原理,给出了不确定噪声协方差矩阵的扰动上界,并在此界限内采用最坏情况下的最优滤波器实现对状态的估计.该设计方案不仅能极小化不确定下的最坏性能.而且能够确保性能指标达到给定的某个自由度.文中给出数值算例表明了设计方案的有效性.     

Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling

In this paper, the problem of non-fragile passive control for Markovian jump systems with aperiodic sampling is investigated. The considered controller is assumed to have either additive or multiplicative norm-bounded uncertainties. A time-dependent Lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non-fragile stochastic passivity of the resultant closed-loop system. Based on the condition, a mode-independent state feedback sampled-data controller is designed such that for all admissible uncertainties the closed-loop system is robustly stochastically passive. Two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques.     

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.     

Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

This article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L₁‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L₁‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

Observer-based dissipative control for Markovian jump systems via delta operators

This paper addresses the issue of observer-based dissipative control problem for a class of Markovian jump systems with random delay via delta operator approach. First, based on the construction of a novel Lyapunov functional together with the use of free-weighting matrix approach, a new set of sufficient conditions is established which ensures the stochastic asymptotic stability and dissipativity of the closed-loop augmented Markovian jump delta operator system. Next, the result is extended to design an observer-based state feedback dissipative control law such that the resulting closed-loop system is stochastically asymptotically stable with the desired dissipative performance index. Further, the existence of control laws is formulated in the form of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Also, the observer and control gains can be calculated by using the solutions of an obtained set of LMIs. It is worth pointing out that the dissipative control problem considered here includes the H_∞ and passivity-based control problems as special cases. Finally, two numerical examples with simulation are presented to demonstrate the effectiveness of the obtained design technique.     

Dissipative control for nonlinear Markovian jump systems with mixed time‐delays: The discrete‐time case

This article is concerned with the dissipative control problem for discrete‐time nonlinear Markovian jump systems subject to both discrete and distributed time‐delays. The purpose is to design a state feedback controller that is capable of guaranteeing the required closed‐loop stability and dissipativity performances simultaneously. By resorting to Lyapunov functional methodology and completing square technique, sufficient conditions are established for the existence of the desired state feedback controller in terms of certain Hamilton‐Jacobi inequalities (HJIs). Within the provided framework, the required controller parameters can be obtained by solving the corresponding HJIs. Finally, two numerical simulation examples are presented to demonstrate the correctness and effectiveness of the developed control paradigm.     

随机非线性扰动下广义马氏跳变系统的控制器设计

针对实际系统中非线性扰动以一定概率存在的情况, 讨论广义马氏跳变系统的控制问题. 首先, 运用Bernoulli 变量描述系统中非线性扰动的存在与否, 建立相应的数学模型, 得到在上述一般条件下系统的随机容许性与解的存在唯一性条件. 然后, 以LMI 形式给出模态依赖和模态独立控制器的存在条件. 与现有结果相比, 所得结果考虑了非线性扰动的存在概率, 具有较小的保守性. 最后, 通过数值例子验证了所得结果的有效性和优越性.

     

Event‐triggered control for networked Markovian jump systems

The problem of H_∞ control for networked Markovian jump system under event‐triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event‐triggered scheme to choose the transmitted data is designed. A Markovian jump time‐delay system model is employed to describe the event‐triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed‐loop system is stable and has a prescribed performance index. A co‐design method for the H_∞ controller and the event‐triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example. Copyright © 2014 John Wiley & Sons, Ltd.