Composite optimal control for singularly perturbed systems with time-delay via successive approximation approach

摘要

The quadratic optimal control problem for linear time-delay singularly perturbed systems is investigated via successive approximation approach (SAA) in this paper. Based on singular perturbation theory, the system is decomposed into two subsystems of a slow-time scale and a fast-time scale. The slow-time scale time-delay optimal control problem is transformed first into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. By using the SAA, the optimal control law of the slow sub-system with time-delay is obtained. Further, the composite control law of the original problem is given. The composite control law consists of non-delay feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. Simulation examples indicate that the SAA is valid and easy to implement.