Adaptive event‐triggered robust H_∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay

Abstract

This paper considers an adaptive event‐triggered robust H∞ control for the Takagi–Sugeno (T‐S) fuzzy under the networked Markov jump systems (NMJSs) with time‐varying delay. First, a new adaptive event‐triggered scheme is developed to guarantee the T‐S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state‐feedback controller (mode‐dependent) in a closed‐loop form for stochastic stability for all admissible parameter uncertainties with an H∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck‐trailer application is used to demonstrate the effectively of the proposed algorithms.

Indefinite LQ optimal control for stochastic Takagi–Sugeno fuzzy system under sensor data scheduling: Finite‐horizon case

“…□ Remark 3. Theorems 1 and 2 imply that the LQ problem (4)-( 5) is well-posed if and only if there exist P i k and F i k satisfying the CDREs in (16). And the feasibility of LMIs ( 22)-( 23) guarantees the existence of optimal solutions.…”

“…Utilizing extended Schur's lemma in [39] with (22), we can easily deduce that the cost function is bounded from below by…”

“…is defined by (16). By repeating the above iteration step by step, the optimal output feedback controller u k can be obtained as (28) for k = 0, 1, … , N.…”

“…In recent years, there have been various attempts to address this limitation by employing the Takagi-Sugeno (T-S) fuzzy model-based technique for stochastic nonlin-ear systems. This approach involves the interpolation of numerous local linear models using IF-THEN fuzzy rules [15][16][17][18]. With the T-S fuzzy model-based approach, precise fuzzy models can be created for nonlinear control systems, ensuring a high level of accuracy compared to the original nonlinear system.…”

Fuzzy‐model‐based robust control of Markov jump nonlinear systems with incomplete transition probabilities and uncertain packet dropouts

“…IT2FMJSs can combine the advantages of IT2FSs and Markov jump systems (MJSs), which can better describe complex nonlinear systems with uncertainties and system mode switching. Over the past decade, many favorable results of fuzzy MJSs (FMJSs) have been reported, including stability [17, 18], stabilization [19], and $$$ {H}_{\infty } $$$ control [20, 21]. However, transition probabilities that govern the dynamic behavior of MJSs have been usually assumed to be completely known.…”