Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

• Published in: International journal of robust and nonlinear control Vol. 33; no. 13; pp. 7700 - 7717
• Main Authors: Feng, Zhiguang, Feng, Bo, Li, Liya, Zhang, Naifu, Jiang, Zhengyi
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.09.2023
• Subjects: asynchronous control; Availability; Dynamical systems; Feedback control; Linear matrix inequalities; Markov chains; Markovian jump systems; Mathematical analysis; Mathematical models; Nonlinear dynamics; Nonlinear systems; reachable set synthesis; Subsystems; T‐S fuzzy model
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6790

This note addresses the asynchronous state‐feedback control (ASC) for delay nonlinear Markovian jump systems (DNMJSs) subject to reachable set boundary. Under taking time‐varying delays and external disturbance into consideration, Takagi‐Sugeno fuzzy model is adopted to approximate the nonlinear dynamics systems. Although the assumption about time‐delay is practical, it will cause subsystem modes to be not synchronous with the controller modes. As a consequence, the description method of the nonsynchronous phenomenon is introduced, which is a hidden Markov model. Furthermore, an available ASC is designed and all reachable states of the system is constrained within the compact ellipsoidal boundary to guarantee the safe operation of the DNMJSs. The existence conditions of the desired ASC are obtained via solving a group of feasible linear matrix inequalities. Finally, some numerical simulations are provided to verify the availability of the proposed method in this article.