Performance verification of low-frequency learning adaptive controllers

While adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady state closed-loop performance is still a challenging problem from the verification and validation standpoint. To that end, we considered a recently developed robust adaptive control methodology called, low-frequency learning adaptive control, and utilize a set theoretic analysis to show that the transitory performance of this approach can be expressed, analyzed, and optimized via a convex optimization problem based on linear matrix inequalities. This key feature of the analysis framework allows one to tune the adaptive control design parameters rigorously so that the tracking error components of the closed-loop nonlinear system evolve in a priori specified region of the state space. Numerical examples are provided to demonstrate the efficacy of the proposed verification and validation architecture.