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Robust Tracking Design Based on Adaptive Fuzzy Control of Uncertain Nonlinear MIMO Systems with Time Delayed States

Tzu-Sung Wu*, Mansour Karkoub, Chien-Ting Chen, Wen-Shyong Yu, Ming-Guo Her, and Jui-Yiao Su
International Journal of Control, Automation, and Systems, vol. 11, no. 6, pp.1300-1313, 2013

Abstract : It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

Keyword : H∞ control, indirect adaptive fuzzy control, MIMO nonlinear systems, Riccati-like equation, time delayed uncertainty, two inverted pendulums on carts system, two-degree-of-freedom mass-spring-damper system, variable structure scheme.

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