Optimal Asynchronous Control of Discrete-Time Hidden Markov Jump Systems With Complex Transition Probabilities

• Published in: IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2024-02, Vol.54 (2), p.1-9
• Main Authors: Tao, Yue-Yue, Wu, Zheng-Guang
• Format: Article
• Language: English
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> mathscr{H}_{\infty}</tex-math> </inline-formula> control; Complex transition probabilities; Cybernetics; hidden Markov model (HMM); Hidden Markov models; Markov analysis; Markov chains; Markov jump systems (MJSs); Markov processes; Stability criteria; Transforms; Transition probabilities; Uncertainty; Upper bound
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2023.3324364

In this article, we focus on the asynchronous \mathscr{H}_{\infty} control problem for discrete-time hidden Markov jump systems (MJSs) with complex mode transition probabilities (C-TPs). The significance of this study can be revealed as follows. First, a hidden Markov model (HMM) is used to estimate the system mode, which cannot always be accurately detected in practical scenarios. Second, the TPs of the Markov process are commonly difficult to be precisely obtained in practical scenarios; hence, some TPs of the Markov process could be unknown or imprecise, resulting in the C-TPs circumstances. Particularly, when taking the HMM into consideration, the C-TPs can also appear in the conditional TPs of the joint process. Therefore, in this work, we consider that the C-TPs may simultaneously exist in both processes of the HMM, which is more practical for hidden MJSs. Additionally, the established results can cover some special cases, for instance, the cases in which C-TPs only exist in one of the processes or neither. The Markov and the joint processes of the HMM are separated by a mode separation strategy so that the C-TPs of them can be, respectively, addressed. Furthermore, only necessary conservatism in dealing with the C-TPs is further introduced. Specifically, when the TPs are perfectly known, the established results can be reduced to an existing result without increasing conservatism. Two examples are presented to demonstrate the effectiveness of the developed results.