Adaptive control for linear parameter-varying systems with application to a VTOL aircraft

Abstract

As a systematic method for gain-scheduling, the linear parameter-varying (LPV) system framework has been widely used for the design of aerospace control systems with large operating envelopes. This paper presents design and analysis of an adaptive control architecture for LPV systems subject to time-varying parametric uncertainties and external disturbances, with both transient and steady-state performance guarantees. We introduce new tools relying on parameter-dependent Lyapunov functions and linear matrix inequality techniques for stability and performance analysis. These tools – limited to linear systems – potentially yield less conservative results than the approach employed for this architecture in previous adaptive control literature based on the small-gain theorem. The transient and steady-state performance of the adaptive closed-loop system, in terms of input and output signals, is quantified with respect to a non-adaptive reference system that depends on the true values of the uncertainties and represents the best achievable performance. It is shown that the transient performance bounds can be made arbitrarily small in the case of zero initialization error for the state predictor and will include additional exponentially decaying terms in the presence of non-zero initialization error. The approach can be used to design an adaptive augmentation of a baseline LPV control system. A simulation example of the longitudinal dynamics of a conceptual Urban Air Mobility aircraft is used to illustrate the efficacy of the proposed framework.