Optimal Tracking Control Problem for Linear State and Control Time-delay Systems

This note focuses on the optimal tracking control (OTC) problem of a class of linear systems with state and control time-delay. First, we change the original system into linear system only with state time-delay by using the time-delay transformation. Then this problem is transformed into a sequence of non homogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms using the successive approximation approach (SAA). Last through a finite iteration of the solution sequence, an approximate solution of asuboptimal tracking control (STC) problem is obtained. Simulation results illustrate that the presented approach is effective.