Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Abstract

Abstract-This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the T-S fuzzy descriptor systems are developed. A two step design is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities, and the results are used to facilitate the development of a single step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.Index Terms-Observer-based stabilization, T-S fuzzy descriptor systems, integral sliding mode control, mechanical systems.

Observer‐based sliding mode control for state‐saturated systems under weighted try‐once‐discard protocol

“…which means that the asymptotic stability of the closed-loop system (10) and 16is attained eventually, and this completes the proof. ▪…”

“…In this case, it is important to estimate the system states by using the measured output. Unfortunately, in the context of SMC problems, the state estimation problem for our addressed networked state-saturated systems becomes much complicated than those investigated in existing works 10,12 since the communication protocol has a major impact on the actually received measurement by the observer. As shown in Figure 2, the measured output y(k) is transmitted to the controller and the observer via a shared communication channel subject to the following WTOD protocol: at each transmission instant, only one sensor node, which has the largest difference between the latest transmitted values and the current values of the signals corresponding to the node, will be granted access to the network, and the other nodes keep the received values unchanged via the buffer 31,32 until the renewed data is arrived.…”

“…The following theorem presents a sufficient condition for guaranteeing the asymptotic stability of the closed-loop system (10) and (16) under the WTOD protocol (7).…”

“…Then, the sliding variable s(k) along the closed-loop system (10) and (16) is forced into the following domain S around the specified sliding surface s(k) = 0:…”

Adaptive multilayer T-S fuzzy controller for nonlinear SISO system optimized by differential evolution algorithm

“…Paper 25 successfully proposed the concept of Multilayer Fuzzy model for identifying uncertain nonlinear MISO system. Furthermore, in order to compensate the uncertainties and guarantee the asymptotic stability, there are many different adaptive fuzzy control methods based on the classic advanced control algorithm such as sliding mode control (SMC) [26][27][28][29][30][31][32] , H 2/ ∞ technique [10][11][12][13] , linearization feedback control [33][34][35][36] , back-stepping technique [37][38][39][40] . However, these above-mentioned techniques require knowing in advance the characteristics of nonlinear uncertain SISO or MIMO system.…”