Sliding Mode Control for Markovian Jump Systems with Generalized Switching

The transition probability synthesis problem is addressed for discrete‐time Markovian jump linear system (MJLS) with state‐dependent multiplicative noises. The proposed mode‐dependent parametric approach is employed to derive the necessary and sufficient condition for ensuring the existence of the stabilizing transition probability matrix (TPM). A key feature here is that the system mode is considered to be unavailable to the controller but can just be observed via a hidden Markov mode detector. To this end, a hybrid design is developed by co‐designing the stabilizing TPM and the asynchronous mode‐dependent state‐feedback controller. A rank‐constrained nonconvex problem is formulated to solve the hybrid design strategy. Specifically, a binary genetic algorithm (GA) is introduced for overcoming the computation difficulties arising from searching optimized mode‐dependent parameters. Finally, two numerical examples are provided to verify the effectiveness and advantages of the proposed hybrid design strategy via GA.

Section: Design Of Stabilizing Tpmmentioning

confidence: 95%

“…Some typical engineering applications of MJLSs can be found in the wind turbine and networked control system [3][4][5]. Meanwhile, some existing results on study-ing the stability analysis and control/filtering issues of MJLSs have been reported in several studies [6][7][8][9][10][11] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Optimized hybrid design with stabilizing transition probability for stochastic Markovian jump systems under hidden Markov mode detector

Jia

Song

Niu

et al. 2021

“…Sliding mode control (SMC), as a powerful robust control strategy in handling external disturbances and parameter uncertainties, has been widely employed to different kinds of systems [16][17][18][19][20][21][22][23]. The key idea of SMC is to utilize a discontinuous control to drive the system state trajectories into the bounded sliding mode region and stay there in the subsequent time.…”

Section: Introductionmentioning

confidence: 99%

Improved event‐triggered sliding mode control of switched systems with disturbances

Wang

Rui

Zhang

2021

This paper is devoted to solving the problem of sliding mode control for discrete-time switched systems with disturbances via an improved event-triggered strategy. First, the switched sliding mode dynamics is obtained based on the pre-designed sliding mode surface. Then, on the basis of the Lyapunov functional technique and the average dwell time approach, sufficient conditions for the existence of the concerned sliding mode dynamics are established. Third, the sliding mode control law is synthesized such that state trajectories of the considered switched system can be driven into the bounded sliding mode region and maintain there subsequently. Moreover, the event-triggered scheme is proposed in close combination with key feature of sliding mode control, which is different from the most existing works. Finally, two examples including a single-link robot arm system are given to show the effectiveness of the proposed design method.

“…The switching among the modes is governed by a Markov process which has discrete and finite state space. Therefore, it could model many dynamic systems [19–23]. In this class of systems, transition rates are the major factors in the jump process.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered stabilization for continuous‐time saturating Markov jump systems with generally uncertain transition rates

Liu

et al. 2020

This paper is concerned with the stabilization for continuous‐time saturating Markov jump system with generally uncertain transition rates (GUTRs) under event‐triggered strategy. In the GUTRs model, the transition rate could be unknown or only its estimated value and estimated error bound are known. In practical systems, actuator saturation commonly exists, which may lead to instability. Event‐triggered strategy is introduced in Markov jump systems to save communication resources. A stochastic stabilization condition is derived for the underlying system considering event‐triggered control and the lower bound of the inter‐event time interval is calculated to avoid Zeno behavior. To obtain the biggest domain of attraction, an optimization algorithm is formulated. Finally, numerical examples are provided to illustrate the application of the given results.