TRANSIENT BOUNDS FOR ADAPTIVE-CONTROL SYSTEMS

Adaptive control systems are essentially nonlinear and mechanisms to a nalyze their stability and transient response typically derive from mo re general nonlinear theories such as small gain arguments or passivit y. In this note, we consider how these theories may be applied to adap tive control to quantify transient response. This involves the explici t description of the constants appearing in the passivity theorem and/ or the small gain theorem which characterize both system gains and ini tial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which co nnects initial state conditions with the input-output analysis. Applyi ng these general theorems to adaptive control, we are able to interpre t the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response . The implication of these sufficient results is that without both bou nds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even tho ugh global convergence and asymptotic performance are guaranteed.