Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization. Specifically, we introduce a piecewise-constant estimation law to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with nominal linear dynamics. In addition, leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques,} we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time. The theoretical development is validated by extensive simulations using the short-period dynamics of an F-16 aircraft.Comment: 28 pages, 9 figure