Approximate Design of Optimal Tracking Controller for Linear Systems with Time-delay

A sensitivity approach designing the optimal tracking controller for a class of linear systems with time-delay is developed. By using the sensitivity approach, an iterative process is proposed to solve the original optimal tracking control (OTC) problem. In the iterative process, both time-delay and time-advance terms are considered as the known additional disturbances so that the original OTC problem is transformed into a sequence of inhomogeneous linear two-point boundary value (TPBV) problems. This approach only requires solving a sequence of linear vector differential equations. The obtained OTC law consists of two linear analytic terms and a compensation term, which is a series sum of the adjoint vectors. A reduced order reference input observer is constructed such that the OTC law is physically realizable. The simulation results demonstrate the effectiveness of the proposed algorithm.