OPTIMAL CONTROL OF UNCERTAIN EULER-LAGRANGE SYSTEMS By KEITH DUPREE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMAL CONTROL OF UNCERTAIN EULER-LAGRANGE SYSTEMS By Keith Dupree May 2009 Chair: Warren E. Dixon Major: Mechanical Engineering Optimal control theory involves the design of controllers that can satisfy some tracking or regulation control objective while simultaneously minimizing some performance metric. A sufficient condition to solve an optimal control problem is to solve the Hamilton-Jacobi-Bellman (HJB) equation. For the special case of linear time-invariant systems, the solution to the HJB equation reduces to solving the algebraic Riccati equation. However, for general systems, the challenge is to find a value function that satisfies the HJB equation. Finding this value function has remained problematic because it requires the solution of a partial differential equation that can not be solved explicitly. Chapter 2 illustrates the amalgamation of optimal control techniques with a recently developed continuous robust integral of the sign of the error (RISE) feedback term. Specifically, a system in which all terms are assumed known (temporarily) is feedback linearized and a control law is developed based on the HJB optimization method for a given quadratic performance index. Under the assumption that parametric uncertainty and unknown bounded disturbances are present in the dynamics, the control law is modified to contain the RISE feedback term which is used to identify the uncertainty. A Lyapunov stability analysis is included to show that the RISE feedback term asymptotically identifies the unknown dynamics (yielding semi-global asymptotic tracking) provided upper bounds on the disturbances are known and the control gains are selected appropriately. A feedforward neural network is then added to the previous