Approximate design of optimal tracking controller for time-delay systems

Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV prob- lems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The com- pensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.