Output Feedback Adaptive Control with Low-Frequency Learning and Fast Adaptation

While adaptive control has been used in numerous applications to achieve system performance without excessive reliance on system models, the necessity of high-gain learning rates for achieving fast adaptation can be a serious limitation of adaptive controllers. Specifically, in safety-critical systems involving large system uncertainties and abrupt changes in system dynamics, fast adaptation is required to achieve stringent tracking performance specifications. However, fast adaptation using high-gain learning rates can cause high frequency oscillations in the control response resulting in system instability. This paper develops an output feedback adaptive control framework for continuous-time, minimum phase multivariable dynamical systems for output stabilization and command following to address the problem of achieving fast adaptation using high-gain learning rates for systems with partial state information. The proposed framework uses a controller architecture involving a modification term in the update law that filters out the high-frequency content in the control response while preserving uniform boundedness of the system error dynamics. The approach is based on a nonminimal state-space realization that generates an expanded set of states using the filtered inputs and filtered outputs, as well as their derivatives, of the original system, and requires knowledge of only the open-loop system’s relative degree and a bound on the system’s order.