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

Abstract

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.

Hybrid asynchronous sliding mode control for hidden Markovian jump systems under optimized design

“…A multiple‐loops linear searching of griding technique as in Reference 13 is a feasible way to preassign these mode‐dependent parameters $$$ {\sigma}_i $$$, $$$ {\gamma}_{2i} $$$, and $$$ {\gamma}_{3i} $$$. However, as pointed in Reference 25, the computation burden will be increased exponentially with the system mode number $$$ N $$$ and the detection mode number $$$ M $$$. Furthermore, to guarantee the nonsingularity of $$$ Z{B}_i $$$ in (16), the trial and error method is a solution as in Reference 20, $$$ Z={\sum}_{i=1}^N\kern.17em {\chi}_i{B}_i^{\mathrm{T}} $$$ with $$$ {\chi}_i $$$ () proper scalars.…”

“…With the aids of the HMMD, asynchronous sliding mode controllers for discrete‐time and continuous‐time MJSs were developed in References 23 and 24, respectively. Recently, an interesting scenario of hybrid design was investigated in Reference 25, in which the transition rates and the asynchronous controller were co‐designed for stochastic MJSs. To the best of our knowledge, the problem of transition rate design for the disturbed systems with matched disturbances has not been studied.…”

“…A natural issue arises whether the disturbed system with matched disturbances can be stabilized by single transition rate synthesis. Obviously, comparing with References 10‐13, 20, 21, and 25, the existences of matched disturbances and mismatched modes will make the hybrid design problem more complex and challenging, which motivates the present research.…”

Observer‐based event‐triggered H‐infinity sliding control of Markovian jump system suffer from actuator attacks

“…The issue of observer design for MJSs was investigated in Jiang et al [10]. For more details, see Cheng et al [11] and Jia et al [12] and references therein. It is commonly acknowledged that the stability attracts the main attention in the analysis and synthesis of a dynamic system.…”

Hybrid‐triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

“…Authors in [2] have applied the hidden Markov model to devise an asynchronous passive controller for MJSs. Jia et al [14] have investigated optimized hybrid design with stabilizing transition probability for stochastic MJSs with hidden Markov mode detector. The work in [15] has applied HMM robust fault estimation to deal with MJSs.…”