A hidden Markov model based control for periodic systems subject to singular perturbations

• Published in: Systems & control letters Vol. 157; p. 105059
• Main Authors: Cheng, Jun, Park, Ju H., Wu, Zheng-Guang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2021
• Subjects: Fading channel; Hidden Markov model; Periodic Lur’e system; Singular perturbation; Hidden Markov model; Fading channel; Periodic Lur’e system; Singular perturbation
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2021.105059

This study analyzes the problem of hidden Markov model based control for periodic systems subject to singular perturbations and Lur’e cone-bounded nonlinearity. Different from the existing time-invariant fading channels, the fading channels are alleviated to be time-varying. Furthermore, to better depict the time-varying property of the fading channels, a novel periodic Markov process framework subject to mean and variance is developed. The highlight of this study lies that the hidden Markov model detector is forwarded to observe the fading channel mode, whose detection probabilities are generalized to be partially recognized. New techniques are developed in dealing with the stochastic Lyapunov functional, and sufficient conditions are gained to ensure the resulting dynamic is stochastically stable. In the sequel, the asynchronous controller parameters are further achieved to reflect the discrepancy between fading channel mode and its detected one. Finally, an application-oriented example is rendered to confirm the effectiveness and applicability of the developed control strategy.