Integrated Adaptive Control and Reference Governors for Constrained Systems With State-Dependent Uncertainties

This paper presents an adaptive reference governor (RG) framework for a linear system with matched nonlinear uncertainties that can depend on both time and states, subject to both state and input constraints. The proposed framework leverages an ( $\mathcal{L}_{1}$ ) adaptive controller ( $\mathcal{L}_{1}$ AC). that compensates for the uncertainties, and provides guaranteed transient performance, in terms of uniform bounds on the error between actual states and inputs and those of a nominal (i.e., uncertainty-free) system. The uniform performance bounds provided by the ( $\mathcal{L}_{1}$ ) AC are used to tighten the pre-specified state and control constraints. A reference governor is then designed for the nominal system using the tightened constraints, and guarantees robust constraint satisfaction. Moreover, the conservatism introduced by the constraint tightening can be systematically reduced by tuning some parameters within the ( $\mathcal{L}_{1}$ ) AC. Compared with existing solutions, the proposed adaptive RG framework can potentially yield reduced conservativeness for constraint enforcement and improved tracking performance due to the inherent uncertainty compensation mechanism. Simulation results for a flight control example illustrate the efficacy of the proposed framework.