Approximately Optimal Disturbance Attenuation for Nonlinear Time-Delay Large-Scale Systems

The optimal control problem for nonlinear time-delay large-scale systems with persistent disturbances is considered. By using the successive approximation approach, 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 differential equations. By iteratively solving the sequence of linear differential equations, an optimal control law is obtained, which consists of analytic linear feedforward, feedback terms and a dynamic compensator. The feedforward term is used for persistent disturbance attenuation and the compensator is for the purpose of compensating nonlinearities and time delays. A suboptimal control law is obtained by truncating a finite term of the adjoint vector sequence as its compensator. An iterative algorithm to obtain the suboptimal control law is proposed. A simulation example illustrates the validity of the algorithm.