Title:  ROBUST ADAPTIVE OPTIMAL CONTROL OF NONLINEAR SYSTEMS IN THE PRESENCE OF PARAMETER UNCERTAINTIES AND UNMODELLED DYNAMICS

Committee: 

Dr. Vela, Advisor

Dr. Verriest, Chair

Dr. F. Zhang

Abstract:

The objective of the proposed research is to design two-layer robust optimal adaptive controllers for nonlinear systems with structured and unstructured uncertainties. The outer layer specifies a quadratic program (QP) to minimize and bound the control signal subject to robust control Lyapunov function (RCLF) and control barrier function (CBF) constraints in which convergence of tracking error trajectories and forward invariance of a safe set is guaranteed. In the inner layer, a concurrent learning (CL) adaptive technique compensates for the unknown dynamics of nonlinear  system with structured/unstructured uncertainties. A robust term robustifies the proposed controllers to disturbances and unmodeled uncertainties.  The unified robust adaptive optimal approaches meet multiple design specifications such as control optimality, tracking performance, dynamic  estimation, safety performance, and robustness to unmodeled dynamics. Stability analyses guarantee uniformly ultimate boundedness (UUB) of all system signals in the presence of modeling error and disturbances. Performance of the proposed controllers is demonstrated through simulation studies, which shows improvements versus baseline methods. Results show that the proposed controllers provide smaller bounds on error trajectories and barrier violation with better control optimality over the baseline approaches in the presence of modeling error and disturbances.