Online Time Delay Identification and Adaptive Control for General Classes of Nonlinear Systems

Abstract

In this dissertation, online identification of time delays is discussed. Specifically, a novel online time delay identification algorithm for nonlinear systems is presented. As a novel departure from the existing literature, in the design of the time delay identification algorithm, time delays are considered as nonlinear parameters effecting the system and nonlinear parameter estimation techniques are adopted. The presented time delay iden~ tification technique is based on a min-max optimization algorithm. The stability of the proposed time delay identification algorithm is investigated via Lyapunov-based stability analysis techniques. It is shown that the developed estimator identifies unknown time delays, upon satisfaction of a nonlinear persistent excitation condition, within a desireq precision that may be adjusted to be very small. The proposed time delay identification method is then modified to be applicable for sig~ nal processing applications. Afterwards, the control of nonlinear systems subject to state delays is considered. The control objective is to ensure output tracking of a time-varying reference trajectory while identifying unknown state delays. Two cases are considered~ First, only the state delays are assumed to be unknown in the nonlinear system dynamics, Second, linear parameters in the system dynamics are assumed to be unknown along witll unknown time delays. To meet the control objectives, the proposed time delay identifica~ tion technique is fused with a control algorithm, and in both cases, both identification anq control objectives are ensured.