Global adaptive control of feedforward systems using dynamic high gain scaling

Abstract

We propose an adaptive control design technique for feedforward systems based on our results on dynamic high-gain scaling techniques for controller design for strict-feedback-type systems. Both the state-feedback and the output-feedback cases are considered. The system is allowed to contain uncertain functions of all the states even in the output-feedback case. Unknown parameters are allowed in the bounds assumed on the uncertain functions appearing in the dynamics. The designed controllers have a very simple structure being essentially a linear feedback with state-dependent dynamic gains and do not involve any saturations or recursive computations. The observer in the output-feedback case is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in the states and the parameter estimation errors (and the observer errors in the case of output-feedback). The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations. The controller design provides strong robustness properties both with respect to uncertain parameters in the system model and additive disturbances. This robustness is the key to the output-feedback controller design.