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

Abstract

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.

Resilient and finite‐time H∞$$ {H}_{\infty } $$ control of semi‐Markov jump systems with both upper and lower thresholds of sojourn time

“…The sojourn time of three modes T 1 , T 2 , and T 3 is considered to take values in Z [3,13] , Z [2,8] , and Z [1,6] respectively. The available STPDFs are chosen as f 12 (𝜏) = 0.6 𝜏−3 ⋅0.4 13−𝜏 ⋅10!…”

“…Thus, semi-Markov jump systems (SMJSs) are developed to compensate these inadequacies in depicting some practical dynamics. [5][6][7][8] Currently, it is found that SMJSs are more effective methods in some modeling scenarios, like epidemiological spread network model, 9 the RLC circuit system 10 and many relevant researches have been conducted.…”

“…Considering that the distribution of the sojourn time of MJSs is memoryless and stochastic in both the discrete‐ and continuous‐time cases, and it is required that all transition probabilities (TPs) should be known with certainty, the further applications of the MJSs are largely constrained. Thus, semi‐Markov jump systems (SMJSs) are developed to compensate these inadequacies in depicting some practical dynamics 5–8 . Currently, it is found that SMJSs are more effective methods in some modeling scenarios, like epidemiological spread network model, 9 the RLC circuit system 10 and many relevant researches have been conducted.…”