Performance Reference Adaptive Control: A Joint Quadratic Programming and Adaptive Control Framework

This paper presents a two-layer robust optimal adaptive control for a class of affine nonlinear systems. The outer later specifies a quadratic program (QP) to optimize the control signal subject to a robust control Lyapunov function (RCLF) constraint. The inner layer employs concurrent learning adaptive laws to estimate the model uncertainty while aiming for RCLF stabilization performance. The resulting concurrent learning-performance reference adaptive control (CL-PRAC) technique compensates for the unknown system dynamics with structured uncertainties. The model estimate informs the outer loop for reduced modeling error in the RCLF structure and enhanced optimality in the face of model uncertainty. The proposed united QP-RCLF+CL-PRAC approach provides uniformly ultimate boundedness of the tracking error and parameter estimation, with exponential convergence rate while minimizing the control effort. A two-sided stability analysis guarantees stability of the proposed system in the presence of control coefficient uncertainty. The case of control saturation constraints is covered in the derivation. Performance of the proposed controller is demonstrated through simulation studies, which show improvements versus a baseline QP-CLF approach.