Suboptimal control for singularly perturbed large-scale systems with time-delay

This paper deals with an optimal control problem for a class of singularly perturbed time-delay large-scale systems. The optimal control laws for the order-reduced slow subsystem with time-delay and fast subsystem are designed, respectively. For the slow subsystem, the sensitivity approach is proposed to solve the coupled two-point boundary value (TPBV) problem with both time delay and advance terms. The TPBV problem is transformed into a decoupled sequence of inhomogeneous linear TPBV problems without time delay and advance terms. By solving the sequence of TPBV problems and Riccati equations, the approximate optimal control law of the original system is obtained. The control law consists of analytic state feedback and a time-delay compensation term which is a series sum of adjoint vectors. The compensation term can be approximately obtained by a recursion formula of adjoint vectors. Numerical examples show that the proposed method is valid.