Universal Adaptive Control of Nonlinear Systems

TLDR: In this paper, a universal adaptive control framework that extends the certainty equivalence principle to nonlinear systems with unmatched uncertainties is developed, which can handle model variations while achieving the desired level of performance.

Abstract: High-performance feedback control requires an accurate model of the underlying dynamical system which is often difficult, expensive, or time-consuming to obtain. Online model learning is an attractive approach that can handle model variations while achieving the desired level of performance. However, most model learning methods developed within adaptive nonlinear control are limited to certain types of uncertainties, called matched uncertainties, because the certainty equivalency principle can be employed in the design phase. This work develops a universal adaptive control framework that extends the certainty equivalence principle to nonlinear systems with unmatched uncertainties through two key innovations. The first is introducing parameter-dependent storage functions that guarantee closed-loop tracking of a desired trajectory generated by an adapting reference model. The second is modulating the learning rate so the closed-loop system remains stable during the learning transients. The analysis is first presented under the lens of contraction theory, and then expanded to general Lyapunov functions which can be synthesized via feedback linearization, backstepping, or optimization-based techniques. The proposed approach is more general than existing methods as the uncertainties can be unmatched and the system only needs to be stabilizable. The developed algorithm can be combined with learned feedback policies, facilitating transfer learning and bridging the sim-to-real gap. Simulation results showcase the method