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1.
This paper considers the tracking control problem for nonlinear Markov jump systems based on T–S fuzzy model approach with incomplete mode information. It is assumed that the mode transition rate matrix is not a priori knowledge and only partial information is available. Moreover, the mode where the system stays when operating is not fully accessible to the designed controller. In this incomplete mode information scenario, a hidden Markov model based mechanism is modified to simulate the mode deficiency mapping. The incomplete transition rate matrix is well defined in the form of a polynomial. Based on this, by constructing a polynomially parameter-dependent Lyapunov matrices and linear matrix techniques, sufficient conditions are established to ensure the stochastic stability and a prescribed tracking performance. The controller design scheme are presented by solving a series of LMIs. Examples are given in the end to illustrate the effectiveness of our proposed results.  相似文献   

2.
In this paper, the problems of stochastic finite-time stability and stabilization of discrete-time positive Markov jump systems are investigated. To deal with time-varying delays and switching transition probability (STP), stochastic finite-time stability conditions are established under mode-dependent average dwell time (MDADT) switching signal by developing a stochastic copositive Lyapunov-Krasovskii functional approach. Then a dual-mode dependent output feedback controller is designed, thus stochastic finite-time stabilization is achieved based on linear programming technique. Finally, two examples are given to show the effectiveness of our results.  相似文献   

3.
The issue of adaptive sliding mode controller design via output knowledge is studied for discrete-time Markov jump systems in this paper by means of using singular system scheme. To force the system state onto the sliding motion, an appropriate switching surface depended on the system output is established. Meanwhile, the reachability of the sliding manifold is guaranteed by synthesizing the robust sliding mode controller and adaptive sliding mode controller for the accessible and inaccessible upper bounds of sliding patch, respectively. By using Lyapunov functional technique, sufficient criteria to guarantee the sliding motion to be stochastically admissible are proposed. Then the reachability conditions of the predesigned switching surface are developed. Finally, simulation results are provided to illustrate the effectiveness of the proposed approach.  相似文献   

4.
In this paper, the problem of reliable controller design for event-triggered singular Markov jump systems with partly known transition probabilities, nonlinear perturbations and actuator faults is studied. To mitigate the burden of data transmissions over network, two event-triggered schemes with different triggering conditions are introduced. The switch law between the two event-triggered schemes is governed by a random variable with Bernoulli distribution. Taking nonlinear perturbations and actuator faults into account, the resulting closed-loop system is converted into a time-delay singular Markov jump system with partly known transition probabilities. Sufficient conditions of stochastically admissible for the resulting closed-loop system are obtained in terms of a group of linear matrix inequalities. The co-design of desirable reliable controller and weighting matrices of event-triggered schemes is presented. Finally, two numerical examples are given to show the effectiveness of the developed results.  相似文献   

5.
This paper deals with the exponential boundary stabilization for a class of Markov jump reaction-diffusion neural networks (MJRDNNs) with mixed time-varying delays, which is described by T-S fuzzy model. It is assumed that observed modes in boundary controller are not synchronized with the system modes. Based on a hidden Markov model (HMM), a novel asynchronous boundary control law is developed by using observed modes. Compared with the existing control strategies for distributed parameter systems, the asynchronous boundary control scheme can not only save the cost of the controller installation, but also bring less conservativeness. A delay-dependent sufficient condition to guarantee the exponentially mean square stability is established for T-S fuzzy MJRDNNs with mixed time-varying delays by constructing a Lyapunov functional and utilizing the vector-value Wirtinger-type inequality. Meanwhile, in order to get the designing scheme of the boundary controller, an equivalent LMI-based sufficient criterion is established. In the end, the effectiveness of the proposed results is illustrated by simulation examples.  相似文献   

6.
This paper addresses the nonstationary quantized control problem for the discrete-time Markov jump singularly perturbed systems (MJSPSs) subject to deception attacks (DAs). The control inputs are characterized by randomly occurring DAs and nonstationary quantization simultaneously, where the DAs are depicted by means of a Bernoulli distributed sequence. By applying a multi-layer structure methodology (MLSM), the nonstationary controllers are devised for MJSPSs. Meanwhile, the correlation among system mode, controller mode, and quantizer mode are portrayed via the nonstationary Markov process. Based on a mode-dependent Lyapunov functional, sufficient criteria are established such that the resulting closed-loop system (CLS) is stochastic mean square exponential ultimately bounded (SMSEUB), and the desired controller is designed. Ultimately, two simulation examples are offered to elaborate on the validity and superiority of the proposed theoretical results.  相似文献   

7.
This paper concerns the indefinite linear quadratic (LQ) optimal control problem for discrete-time singular Markov jump systems (MJSs) with finite and infinite horizon, where the weight matrices for state and control of cost function are all indefinite. Firstly, the indefinite LQ problem for singular MJSs is equivalently transformed into indefinite LQ problem for MJSs under a series of equivalent transformations. Then, the sufficient and necessary condition is proposed for the solvability of finite horizon case, the optimal control and optimal cost value are given, and the resulting optimal closed-loop system is regular, casual. Next, some sufficient and necessary conditions are obtained to ensure the transformed equivalent LQ problem for MJSs to be definite one, which can guarantee the generalized algebraic Riccati equation with Markov jump has a unique semi-positive definite solution. Meanwhile, the optimal control and nonnegative optimal cost value in infinite horizon are acquired, and the resulting optimal closed-loop system is stochastically admissible. Finally, three examples are presented to illustrate the theoretical results.  相似文献   

8.
This paper mainly concerns N-step off-line suboptimal predictive controller design for discrete nonhomogeneous Markov jump systems, in which the Markov chains are time-varying transition probabilities matrix modeled as a polytope. The design procedure is divided into N-step, more precisely, the first is to design the Nth step when the changes of Euclidean form of mode-dependent feedback law between the Nth and the (N+1)th asymptotically stable mode-dependent ellipsoids are less than the given accuracy. Then the N  th asymptotically stable mode-dependent invariant ellipsoid is defined. In the previous (N−1)(N−1) steps, an off-line mode-dependent predictive controller is designed to drive the state to this small area including the origin. Compared with on-line MPC algorithm, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One numerical example is presented to illustrate the validity of the developed results.  相似文献   

9.
This paper is concerned with the observer-based H∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.  相似文献   

10.
In this paper, an asynchronous sliding mode control design method based on the event-triggered strategy is proposed for the continuous stirred tank reactor (CSTR) under external disturbance. Firstly, with the purpose of appropriately modeling the multi-mode switching phenomenon in the CSTR caused by the fluctuation of temperature and concentration, the Markov process is applied. Secondly, the asynchronous switching characteristics are introduced to describe mismatch between the controller and the system, which caused by some factors such as signal transmission delay and packet dropout. In order to effectively estimate the system states that cannot be measured in real time, an observer based on the event-triggered strategy is proposed, which also can reduce the computational cost. In addition, a sliding mode controller is designed to ensure the dynamic stability and the sliding dynamics is reachable in a finite time. Finally, the effectiveness of the proposed method is verified by simulation experiments.  相似文献   

11.
This paper deals with the problem of stabilization via synchronous state-feedback control for two-dimensional (2-D) discrete-time Roesser systems with stochastic parameters involving switchings and multiplicative stochastic noises. The switching process is driven by an inhomogeneous Markov chain whose transition probability matrix is piecewise time-invariant and external disturbances are of the type of white noises, which get multiplied into both system state and input vectors. Stability and tractable controller design conditions are derived based on a 2-D mode-dependent Lyapunov function approach, which are validated by a numerical example with simulations.  相似文献   

12.
This paper studies the E-exponential stability of mode-dependent linear switched singular systems with stable and unstable subsystems. First, by constructing an appropriate multiple discontinuous Lyapunov function, new sufficient conditions of E-exponential stability for linear switched singular systems are established. Considering the feature of mode-dependent average dwell time switching, we adopt the switching strategy where fast switching and slowing switching are respectively applied to unstable and stable subsystems. Compared with the existing results, our approach is more flexible and tighter bounds can be obtained. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.  相似文献   

13.
This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.  相似文献   

14.
The issue of finite-time sliding mode control (SMC) is studied for a class of Markov jump systems, in which parameter uncertainties, external disturbances and time-varying delay are considered. Firstly, a suitable observer-based SMC law is devised so that state trajectory of the system can reach the designed sliding mode surface in finite-time, the gain of the controller is asynchronous to the mode of original system. Meanwhile, the sufficient conditions of finite-time boundedness in the sliding phase and reaching phase are derived by the time partition strategy. Moreover, the gains of the observer and the observer-based controller will be acquired by using the linear matrix inequalities tool. In fine, emulation products are used to confirm the merits of the SMC strategy.  相似文献   

15.
In this article, the fault-tolerant control is investigated for the spacecraft attitude control system described by a linearized model with Markovian switching. First, the evolution of sudden failures of the spacecraft’s actuators is described by a Markov process. Then, the mathematical model of the spacecraft attitude control system with the Markov jump characteristic fault is established. Taking the uncertainty of the system model and external interference into consideration, a fault-tolerant control scheme is proposed for the established spacecraft attitude control system with the Markov jump characteristic fault by using the sliding mode control technique. Compared with some existing sliding mode controller design methods, the proposed method requires a less total number of LMIs to be solved. The stability and reachability of the resulting closed-loop system under the presented sliding mode control scheme are proven by applying the Lyapunov stability theory. Finally, some simulation results are provided to show the effectiveness and advantages of the proposed control method for spacecraft attitude control.  相似文献   

16.
This paper is concerned with the problem of event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties. The event-triggered mechanism is introduced to save the limited communication bandwidth resource and preserve the desired system performance. The phenomenon of randomly occurring parameter uncertainties is considered to increase utilizability of the proposed method. To describe such a randomly occurring phenomenon, some mutually independent Bernoulli distributed white sequences are adopted. A mode-dependent state estimator is designed in this paper, which ensures that the estimation error system is extended stochastically dissipative. By using the Lyapunov–Krasovskii functional approach and an optimized decoupling approach, an expected state estimator can be built by solving some sufficient conditions. Two numerical examples are presented to demonstrate the correctness and effectiveness of the proposed method.  相似文献   

17.
This article investigates the control problem of networked Markov jump systems (MJSs). First, to describe the asynchronization between the plant modes and the controller modes in MJSs, the hidden Markov model is introduced and the asynchronous control technique is developed. Next, the dynamic event-triggered mechanism (ETM) is utilized to decrease the frequency of data transmission. Moreover, the round-robin protocol (RRP) is introduced to reduce the amount of communicated data by allowing only one node to access the network. At last, the concept of input-output finite time stability (IO-FTS) is introduced and taken into consideration in the controller design. The highlight of this work is the introduction of both the dynamic ETM and the RRP to alleviate the communication load. Finally, a simulation example is proposed to illustrate the effectiveness of the theoretical results.  相似文献   

18.
This paper studies the high-order moment control problem for discrete-time Markov jump linear systems (MJLSs) with certain dynamic response performance and disturbance rejection specifications. An appropriate cumulant generating function is employed to express the original stochastic system in high-order component form. This facilities the high-order moment stabilization of MJLSs. Moreover, a pole region assignment approach is utilized to ensure desired dynamic response specifications with a certain attenuation rate. An arithmetic and geometric inequality approach is utilized to extract sufficient conditions ensuring the designed controller existence. These conditions ensure the high-order moment steady-state property and certain dynamic specifications for the MJLSs. The effectiveness of the proposed method is demonstrated through numerical and practical examples.  相似文献   

19.
The dissipative synchronization problem of delayed Markov jump switched neural networks (MJSNNs) under state-dependent switching by the event-triggered gain-scheduling control scheme is studied in this paper. By the introduction of a Markov jump model, which is used to depict the random variation wherein the connection of MJSNNs, the issues we study can take more generality. Via constructing suitable Lyapunov–Krasovskii functionals (LKFs) and applying some matrix inequality scaling methods, sufficient conditions for dissipative synchronization of delayed MJSNN are established. According to such criteria, the event-triggered gain-scheduling control scheme is adopted to design a controller with less terminal communication costs. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.  相似文献   

20.
In this paper, the problem of asynchronous H∞ filtering for singular Markov jump systems with redundant channels under the event-triggered scheme is studied. In order to save the resource of bandwidth limited network and improve quality of data transmission, we utilize event-triggered scheme and employ redundant channels. The redundant channels are modeled as two mutually independent Bernoulli distributed random variables. To formulate the asynchronization phenomena between the system modes and the filter modes, the hidden Markov model is proposed so that the filtering error system has become a singular hidden Markov jump system. The criterion of regular, causal and stochastically stable with a certain H∞ performance for the filtering error system has been obtained. The co-design of asynchronous filter and the event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. Two examples are given to show the effectiveness of the proposed method.  相似文献   

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