Transient bounds for adaptive control systems

Adaptive control systems are essentially nonlinear, and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. The authors consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and for the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input/output analysis. Applying these general theorems to adaptive control, one is able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response