Adaptive Certainty-Equivalence Control With Regulation-Triggered Finite-Time Least-Squares Identification, Part II: Analysis

Abstract: We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the conventional adaptive control proofs, where the Lyapunov analysis either encompasses the complete closed-loop state or is done in multiple steps through comparison or Gronwall-Bellman lemmas. In addition, we present a convenient algorithm for checking our parameter-observability assumption, which involves repeated Lie derivatives of appropriate vector fields and can be applied to the class of nonlinear control systems for which at most one unknown parameter appears in each differential equation.