Approximately optimal tracking controller design for nonlinear interconnected large-scale systems with time-delays

The optimal tracking control problem for nonlinear interconnected large-scale systems with time-delays is considered. By using a successive approximation approach (SAA), a high order, coupled, nonlinear two-point boundary value (TPBV) problem with both time-delay and time-advance terms, which is derived from the necessary condition of the original optimal tracking control problem, is transformed into a sequence of linear decoupled TPBV problems. By iteratively solving the linear TPBV sequence, the original optimal tracking control problem is approximately solved. The optimal tracking controller designed consists of an accurate linear term and a compensation term for nonlinearity and time-delays, which is the limit of the adjoint vector sequence. An approximately optimal tracking controller (AOTC) is designed by truncating a finite iterative result of the adjoint vector sequence as its compensation term. An algorithm to design the AOTC is then presented. A numerical example illustrates the validity of this approach.