Dynamic high gain scaling: an application to robust adaptive output feedback for feedforward systems

We propose an adaptive output feedback control design for global asymptotic stabilization of feedforward systems based on our recent results on dynamic high gain scaling based controller design for strict-feedback systems. The system is allowed to contain uncertain functions of all the states and the input as long as they satisfy certain bounds. Unknown parameters are allowed in the bounds assumed on uncertain functions. If the uncertain functions involve the input, then the output-dependent functions in the bounds 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 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 unmeasured states is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in state estimates, observer errors, and parameter estimation error. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations. The controller provides strong robustness properties both with respect to uncertain parameters and additive disturbances. This robustness is the key to the output feedback controller design.