Successive Approximation Procedure of Optimal Control for Nonlinear Interconnected Large-Scale Systems with Time-Delays

The optimal control problem for nonlinear interconnected large-scale dynamic systems with time-delays is considered. A successive approximation procedure (SAP) designing optimal controller is proposed with respect to a quadratic performance index. By using a successive approximation approach (SAA), the 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 control problem, is transformed into a sequence of linear decoupled TPBV problems. The optimal control law obtained consists of an accurate linear term and a compensation term which is the limit of the adjoint vector sequence. A suboptimal control law is obtained by truncating a finite iterative result of the adjoint vector sequence as its compensation term. A SAP algorithm to obtain the suboptimal control law is presented. A numerical example illustrates this approach