## Adaptive fuzzy control of a class of MIMO nonlinear systems.(English)Zbl 1142.93365

Summary: This paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within these schemes, fuzzy systems are employed to approximate the plant’s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors. By using a regularized matrix inverse, a stable well-defined adaptive controller is firstly investigated. Then, in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values, a second adaptive controller is proposed. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability and asymptotic convergence to zero of tracking errors can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

### MSC:

 93C42 Fuzzy control/observation systems 93C40 Adaptive control/observation systems
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### References:

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