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.     

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.     

A ROBUST ADAPTIVE CONTROL DESIGN FOR A CLASS OF UNCERTAIN NONLINEAR MARKOVIAN JUMP SYSTEMS

A direct robust adaptive nonlinear control scheme for a class of uncertain nonlinear Markovian jump systems with nonlinear state‐dependent uncertainty is presented. The proposed scheme is Lyapunov‐based and guarantees the global uniform ultimate boundedness of the closed‐loop system in the mean sense. A numerical example is given to demonstrate the validity of the results.     

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.     

Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays

This article discusses the robust stability problem for a class of uncertain Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent time delays. The transition probabilities of the mode jumps are considered to be partly unknown, which relax the traditional assumption in Markovian jump systems that all of them must be completely known a priori. The mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jump modes. By employing the Lyapunov functional and linear matrix inequality approach, some sufficient criteria are derived for the robust stability of the underlying systems. A numerical example is exploited to illustrate the developed theory.     

Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control.

This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.     

Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay

A prescribed performance adaptive neural tracking control problem is investigated for strict-feedback Markovian jump nonlinear systems with time-varying delay. First, a new prescribed performance constraint variable is proposed to generate the virtual control that forces the tracking error to fall within prescribed boundaries. Combining with the approximation capability of neural networks and backstepping design, the adaptive tracking controller is designed. The designed controller is independent on time delay by constructing appropriate Lyapunov functions to offset the unknown time-varying delays. It is proved that the closed-loop system is uniformly ultimately bounded in probability, and that both steady-state and transient-state performances are guaranteed. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

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.     

Stochastic stability of semi‐Markovian jump systems with mode‐dependent delays

Semi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching

An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H_∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov–Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.     

一类非线性不确定系统的最优自适应控制

研究了一类含有系统扰动，并且状态项与控制项中同时含有未知参数的非线性系统的反馈稳定问题.在控制器的设计中，将原系统的自适应稳定问题转化为扩展系统的非自适应稳定问题，并利用扩展系统的鲁棒控制Lyapunov函数，设计出使原系统自适应稳定的控制律.进一步，利用逆最优的方法，证明了该控制律同时也是满足某种性能指标的最优控制。     

On exponential stability of neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates

The exponential stability for neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates is investigated in this paper. With creative Lyapunov functional and novel matrix inequalities analysis, delay-range-dependent and rate-dependent exponential stability conditions are presented by reciprocally convex lemma and free weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

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.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

一类非线性系统的自适应模糊控制

针对一类非线性系统,利用模糊推理系统对非线性函数的逼近能力,导出基于Ｌｙａｐｕｎｏｖ稳定性理论的自适应控制器,不但能解决这类非线性系统的跟踪问题,而且可保证闭环系统的稳定性。仿真结果表明这一算法的有效性。     

Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays

The notions of the practical stability in probability and in the pth mean, and the practical controllability in probability and in the pth mean, are introduced for some stochastic systems with Markovian jump parameters and time-varying delays. Sufficient conditions on such practical properties are obtained by using the comparison principle and the Lyapunov function methods. Besides, for a class of stochastic nonlinear systems with Markovian jump parameters and time-varying delays, existence conditions of optimal control are discussed. Particularly, for linear systems, optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters.     

具有非线性扰动的网络控制系统的鲁棒稳定化

针对一类具有随机时延和非线性扰动的网络控制系统,利用变采样周期的方法,将连续被控对象离散化,使网络控制系统建模为部分转移概率未知的非线性Markov跳变系统.通过随机Lyapunov方法,给出保证整个闭环系统随机稳定的充分条件,同时得到非线性扰动项的最大界.仿真算例表明了所提出方法的有效性.     

基于广义模糊双曲正切模型的自适应控制器

针对一类非线性函数未知的非线性离散系统，提出一种新的基于广义模糊双曲正切模型的参考模型自适应控制器设计方法，并利用Lyapunov稳定性理论证明了该控制器是全局渐近稳定的．仿真例子证明了该方法的有效性．     

Robust control of uncertain discrete-time Markovian jump systems with actuator saturation

In this paper, the robust stochastic stabilization problem for the class of discrete-time uncertain Markovian jump linear systems (MJLS) with actuator saturation is considered. The definition of domain of attraction in mean square sense (DoA-MSS) is introduced to analyze the stochastic stability of the closed-loop system. By using a class of stochastic Lyapunov function which is dependent on the jump mode and saturation function, design procedures for both the mode-dependent and mode-independent state feedback controllers are developed based on the Linear Matrix Inequality (LMI) approach. Finally, a numerical example is provided to show the usefulness of the proposed techniques.     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.