Delay Robustness and Compensation in L₁ Adaptive Control

Stability analysis of an L1 adaptive control design decomposes into i) the derivation of an inequality condition imposed on a filter in the control channel that guarantees transient performance bounds on the state and control input for a theoretical nonadaptive reference system, and ii) a Lyapunov-type proof of the decay of a predictor error as the inverse square root of the adaptive gain, which in turn can be made arbitrarily large without sacrificing robustness to time delay in the control input. This paper reviews recent results on the robustness to input and communication time delays for L1 control systems with uncertain nonlinearities and in nontrivial network configurations, as well as a possible scheme for compensating for large, constant input delays.