Verifiable frequency-limited adaptive control performance based on linear matrix inequalities

Adaptive controllers are often criticized for the lack of clear and easy verification procedures that relate design parameters to time domain performance especially during transients. For this reason it is a challenge to rigorously certify existing adaptive control algorithms. To that end, we propose a validation framework where stability and performance requirements are formulated in terms of Linear Matrix Inequalities. This brings the advantage that adaptive controller design and verification can be analyzed and optimized via the solution of a convex optimization whose objective is to guarantee the evolution of the error components within an a-priori specified domain. This approach was cast to verify the performance of the recently introduced Frequency-limited adaptive control scheme. A detailed case study is presented to show the efficacy of the proposed verification architecture.