Optimal Adaptive Regulation of Uncertain Linear Continuous-time Systems with State and Input Delays

In this paper, the optimal adaptive regulation of uncertain linear continuous-time systems with state and input delays is introduced using state feedback. First, an adaptive identifier is proposed to estimate the system dynamics. Subsequently, by using a quadratic cost function, a Bellman type equation is derived to obtain the optimal regulation via stationarity condition. Finally, the adaptive identifier and the optimal approach are integrated together to design the optimal adaptive regulator in the presence of uncertain system dynamics. The Lyapunov theory is utilized to show the boundedness of the state vector, parameter estimation and identification errors when the initial parameters lie within a compact set. A simulation example is employed to verify the effectiveness of the proposed approach.