A High-Gain Scaling Technique for Adaptive Output Feedback Control of Feedforward Systems

Abstract

In this note, we propose an adaptive output feedback control design technique for feedforward systems based on our recent results on dynamic high-gain scaling techniques for controller design for strict-feedback systems. The system is allowed to contain uncertain functions of all the states and the input as long as the uncertainties satisfy certain bounds. Unknown parameters are allowed in the bounds assumed on the uncertain functions. If the uncertain functions involve the input, then the output-dependent functions in the bounds on the uncertain functions need to be polynomially bounded. It is also shown that if the uncertain functions can be bounded by a function independent of the input, then the polynomial boundedness requirement can be relaxed. 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 utilized to estimate the unmeasured states is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in the state estimates, the observer errors, and the parameter estimation error. 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. Global asymptotic results are obtained.