Hidden Markov model based control for singular Markov jump systems

A hidden Markov model based control strategy is proposed to ensure the exponential mean-square admissible (EMS-admissible) of singular Markov jump systems (SMJSs) with mode-dependent singular matrix in this paper. The discontinuities caused by the mode-dependent singular matrix and Markov jump switching are investigated to make the results more practical. Concrete controller designing process is presented to tackle the instabilities brought by the hidden Markov model and the discontinuities. A new kind of Lyapunov function is constructed to characterize the switching features presented by Markov jump system and hidden Markov model based controller, which derives the stability conditions of the SMJSs. Then, a linearization strategy is proposed to reduce the coupled terms generated by the hidden Markov model. The hidden Markov model based controller is further designed based on the established conditions to ensure the EMS-admissible of the considered SMJSs. A numerical example and a direct current (DC) motor example are given to illustrate the effectiveness of the control approach.     

A computational study of optimal control of Markov jump systems

This paper considers a class of optimal control problems governed by Markov jump systems. Our focus is to develop a computational method, based on the control parametrization approach, for solving this class of optimal control problems. Due to the existence of the continuous-time Markov chain, the optimal control problem under consideration is a stochastic optimal control problem, and hence the control parametrization technique cannot be applied directly. For this, a derandomization approach is introduced to obtain a representative deterministic optimal control problem. Then, the control parametrization method is applied to obtain an approximate finite dimensional optimization problem which can be computed numerically using the gradient-based optimization method. For this, the gradient formulas of the cost function and the constraint functions with respect to control variables are derived. Finally, a practical application involving a RLC circuit model is solved using the method proposed.     

Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

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.     

Fuzzy-model-based tracking control of Markov jump nonlinear systems with incomplete mode information

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.     

Protocol-based control for wind turbine generator systems with semi-Markov jump parameters

This paper is concerned with the protocol-based control design problem for wind turbine generator systems (WTGSs) via a proportional-integral observer. Considering the variable actual wind speed, the operation points of WTGSs between different subareas are described by a semi-Markov jump process. To efficiently modulate transmission frequency, an adaptive-memory event-triggered protocol (AMETP) is constructed using a sequence of previously broadcasted packets and adaptive triggering thresholds, resulting in better dynamic performance. Benefitting from the parameter-dependent Lyapunov stable theory, some sufficient criteria are formulated for the stochastic stability of the closed-loop systems. At last, the feasibility of the presented approach is tested via a numerical example.     

Sliding mode output-feedback control of discrete-time Markov jump systems using singular system method

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.     

Non-fragile guaranteed cost control for networked nonlinear Markov jump systems under multiple cyber-attacks

This paper is concerned with the problem of non-fragile guaranteed cost control (GCC) for networked nonlinear Markov jump systems subject to multiple cyber-attacks, which are characterized by Takagi–Sugeno (T–S) fuzzy model with time-varying delay. Specifically, a variety of cyber-attacks, including deception attacks and Denial-of-Service (DoS) attacks, are considered, which occur in the forward and feedback communication links, respectively. To achieve stochastic stability under guaranteed cost function (GCF), the paper proposes a Lyapunov–Krasovskii (L–K) function approach. The approach derives sufficient conditions for stochastic stability, and obtains non-fragile controller gains and the uniform upper bound of the GCF using linear matrix inequalities (LMIs) technique. Finally, the effectiveness of the proposed algorithm is evaluated by simulation experiment.     

Event-triggered H∞ control for network-based uncertain Markov jump systems under DoS attacks

This paper investigates the event-triggered $H_{\infty }$ control problem for network-based Markov jump systems subject to denial-of-service (DoS) attacks. In order to reduce the amount of signal transmission, the event-triggering scheme (ETS) is adopted between sensor and controller. Due to DoS attacks invalidating data over networks, a new switched time-delay Markov jump model with unstable subsystems is developed based on state feedback controller. Then with the help of piecewise Lyapunov-Krasovskii functional method, a set of sufficient conditions incorporating constraints of DoS attacks are provided, which guarantees that the resulting switched time-delay Markov jump system is stochastically stable with a certain $H_{\infty }$ performance. Subsequently, we present criterions to obtain the parameters of state feedback gain and ETS. Finally, an example is provided to show the effectiveness of the proposed method.     

Nonstationary quantized control for discrete-time Markov jump singularly perturbed systems against deception attacks

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.     

Observer-based finite-time asynchronous sliding mode control for Markov jump systems with time-varying delay

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.     

Bivariate grid-connection speed control of hydraulic wind turbines

The requirement for An electrical grid-connected wind turbine is that the synchronous generator speed is stable within a required speed range for the electrical grid. In this paper, a hydraulic wind turbine (HWT) system is considered, and the working principle and working conditions of the HWT are introduced. A novel speed control method is proposed in this paper, using both a proportional flow control valve and a variable displacement motor, which are adjusted in combination to control the speed of the HWT. By establishing a state space model of the HWT and solving the nonlinear system with a feedback linearization method, a bivariate tracking controller is constructed to realize accurate speed control under fluctuating wind speed and the load disturbance conditions. The effectiveness of the control method is verified by simulation, but experimental results highlight problems with the method. The theoretical controller is simplified to reduce sensitivity to measurement noise and modeling error. The control effect has been improved to some extent, but it is limited. Based on these results, combined with the sliding mode variable structure control method and the feedback linearization method to solve the problem of measurement noise and modeling error, and the effectiveness of the control law is finally verified experimentally. It lays a theoretical foundation for the practical application of HWT.     

Finite-time control for periodic systems with Markov jump sensor nonlinearities and random input gains

Finite-time control for periodic systems with sensor nonlinearities and random input gains is addressed in this work. The variation of sensor nonlinearities is modeled by a Markov chain, and a stochastic variable is used to describe the influence of the actuator. A mode- and sensor nonlinearity-dependent non-fragile controller is designed to improve the performance and the non-fragility of the controller. The finite-time boundedness of the closed-loop system is ensured by a sufficient condition, the corresponding controller is then designed. Finally, the effectiveness of the developed results is illustrated by a numerical example.     

Input-output finite-time control of Markov jump systems with round-robin protocol: An dynamic event-triggered approach

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.     

Finite and infinite horizon indefinite linear quadratic optimal control for discrete-time singular Markov jump systems

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.     

High-order moment stabilization for Markov jump systems with attenuation rate

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.