LYAPUNOV-BASED CONTROL OF SATURATED AND TIME-DELAYED NONLINEAR SYSTEMS By NICHOLAS FISCHER 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 LYAPUNOV-BASED CONTROL OF SATURATED AND TIME-DELAYED NONLINEAR SYSTEMS By Nicholas Fischer December 2012 Chair: Warren E. Dixon Major: Mechanical Engineering Time delays and actuator saturation are two phenomena which affect the performance of dynamic systems under closed-loop control. Effective compensation mechanisms can be applied to systems with actuator constraints or time delays in either the state or the control. The focus of this dissertation is the design of control strategies for nonlinear systems with combinations of parametric uncertainty, bounded disturbances, actuator saturation, time delays in the state, and/or time delays in the input. The first contribution of this work is the development of a saturated control strategy based on the Robust Integral of the Sign of the Error (RISE), capable of compensating for system uncertainties and bounded disturbances. To facilitate the design of this controller and analysis, two Lyapunov-based stability corollaries based on the LaSalleYoshizawa Theorem (LYT) are introduced using nonsmooth analysis techniques. Leveraging these two results, a RISE-based control design for systems with timevarying state-delays is developed. Since delays can also commonly occur in the control input, a predictor-based control strategy for systems with time-varying input delays is presented. Extending the results for time-delayed systems, a predictor-based controller for uncertain nonlinear systems subject to simultaneous time-varying unknown state and known input delays is introduced. Because errors can build over the deadtime interval when input delays are present leading to large actuator demands, a predictorbased saturated controller for uncertain nonlinear systems with constant input-delays