Abstract
In this paper, a robust adaptive fuzzy controller is designed for the output tracking control problem of mu lti -input mult i-output (MIMO) nonlinear systems with higher-order and un matched uncertainties. For real mechanical systems, the strength of the unmatched uncertainties is bounded by the pth-order polynomials in states, in contrast to other works assuming that these uncertainties are bounded by the first-order polynomials in states. Based on the combination of the H ∞ optimal control with fuzzy systems and some feasible adaptation laws, the proposed robust adaptive fuzzy controller can not only guarantee that all the signals in the whole closed-loop systems are bounded, but also obtain that the output tracking performance of M IMO nonlinear uncertain systems is well established. A series of computer simulat ions are illustrated to demonstrate the validity of the proposed control scheme.
Highlights
The adaptive control of nonlinear systems has attracted a lot of attention, and significant progress has been made in recent years and novel techniques facilitated by advances in geometric nonlinear control theory and in particular input-output feedback linearizat ion method[1,2]
The output tracking control problem of MIM O nonlinear systems with higher-order and unmatched uncertainties has been studied in this paper
In the proposed design method, fuzzy logic systems are used to estimate the part of unknown nonlinear functions, and the robust controller that combines the H ∞ optimal control with adaptive laws can deal with unmatched uncertainties and fuzzy approximat ion errors
Summary
The adaptive control of nonlinear systems has attracted a lot of attention, and significant progress has been made in recent years and novel techniques facilitated by advances in geometric nonlinear control theory and in particular input-output feedback linearizat ion method[1,2]. In[19, 20], based on feedback linearization technique, adaptive fuzzy control schemes have been introduced to deal with nonlinear systems Ho wever, their results were valid while the controlled nonlinear systems did not include the unmatched uncertainties. The fu zzy systems and some adaptive laws are applied to approximate the unknown nonlinear functions and estimate the upper bounds of the International Journal of Control Science and Engineer ing 2012, 2(6): 172-180 unknown uncertainties, respectively These unmatched uncertainties including modeling errors (fu zzy system appro ximation errors) and parameter variations, etc., can lead to the instability of the closed-loop system; a robust compensator is designed by H ∞ control technique to reject this kind of uncertainties.
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