Robustness Improvement of Computationally Efficient Cooperative Fuzzy Model Predictive-Integral Sliding Mode Control of Nonlinear Systems

Abstract

This paper introduces a systematic and comprehensive method to design a constrained fuzzy model predictive control (MPC) cooperated with integral sliding mode control (ISMC) based on the Takagi-Sugeno (T-S) fuzzy model for uncertain continuous-time nonlinear systems subject to external disturbances. The proposed controller benefits from the robustness, optimality, and practical constraints considerations. The robustness against the uncertainties and matched external disturbances is achieved by the proposed ISMC without iterative calculation for obtaining the robust invariant set. The MPC schemes are designed separately based on the both quadratic and non-quadratic Lyapunov functions. By the proposed MPC, the states of the system reach the desired values in the optimal, constrained, and robust manner against the unmatched external disturbances. New linear matrix inequalities (LMIs) conditions are proposed to design both the proposed MPC schemes. Also, the practical constraints on the control signals are guaranteed in the design procedure based on the invariant ellipsoid set. To evaluate the effectiveness of the suggested strategy, some simulation and experimental tests were run. INDEX TERMST-S fuzzy models (TSFMs), Model predictive control (MPC), Integral sliding mode control (ISMC), DC-DC buck converter, Flexible joint robot.

Optimal constrained integral sliding mode control design for fuzzy-based nonlinear systems

“…5. In comparison with the MPC approaches (Farbood et al, 2021a(Farbood et al, , 2021bShen et al, 2020), (a) the computational burden is decreased and (b) the robust performance of the proposed controller is improved, (c) by the proposed method, an iterative calculation for the robust invariant set is not required.…”

Relaxed nonquadratic H∞ robust constrained event-triggered fuzzy controller design for discrete-time nonlinear systems

“…In some of the existing studies that are considered the limitations of the controller, online computation is needed. For example, in the model predictive control (MPC)-based methods (Chen et al, 2023;Farbood et al, 2021Farbood et al, , 2022Homaeinezhad and FotoohiNia, 2023) to calculate the constrained control signal, an online-based optimization problem must be solved. Therefore, the computational burden and the conservatism are increased.…”

“…In the existing studies (Cai et al, 2020;Chaibi et al, 2020;Du et al, 2019;Lian et al, 2019;Zheng et al, 2020), the limitations of the amplitude and rate of the control signals are not considered. To achieve a constrained performance in the onlinebased solving optimization problem methods (Chen et al, 2023;Farbood et al, 2021Farbood et al, , 2022Homaeinezhad and FotoohiNia, 2023;Teng et al, 2018) the computational burden is very high which leads to difficulty in the real-time implementation of the control system. In Echreshavi et al (2021) and , the controller gains to guarantee the closed-loop stability of the system are calculated based on the quadratic Lyapunov function which is a highly conservative approach.…”

“…In Echreshavi et al (2021) and , the controller gains to guarantee the closed-loop stability of the system are calculated based on the quadratic Lyapunov function which is a highly conservative approach. In some of the existing methods (Farbood et al, 2021(Farbood et al, , 2022Wang and Yang, 2019), the robustness against the parameter uncertainties or external disturbances is not guaranteed and the studied system classes are specific. Since the developed methods in Angulo et al (2019), Cai et al (2020), Chaibi et al (2020), Du et al (2019), Lian et al (2019), andSaifia et al (2020) are based on time-triggering, the information transmission numbers are high.…”

“…Despite Cai et al (2020), Chaibi et al (2020), Du et al (2019), Lian et al (2019), Zhang and Dong (2021), and Zheng et al (2020), the amplitude and rate constraints of the control signal are investigated in the procedure of the proposed method in an offline scheme. Consequently, the computational burden of the proposed approach is less than the constrained online-based control methods (Chen et al, 2023;Farbood et al, 2021Farbood et al, , 2022Homaeinezhad and FotoohiNia, 2023). Compared with Cai et al (2020), Chaibi et al (2020), Du et al (2019), Lian et al (2019), andZheng et al (2020) to reduce the communication burden; an ETC is designed to consider the amplitude and rate limitations of the controller, simultaneously for the TSFMbased nonlinear system.…”