Approximate Optimal Control for a Class of Singularly Perturbed Nonlinear Time-delay Systems

The quadratic optimal control problem for a class of singularly perturbed nonlinear time-delay systems is investigated. Based on successive approximation approach (SAA), the reduced order nonlinear time-delay optimal control law is achieved by solving a decoupled sequence of inhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The obtained composite control law of the original problem consists of accurate state feedback terms and a nonlinear time-delay compensation term, which is the limit of the adjoint vector sequence. The proposed algorithms not only solve optimal control problems in the singularly perturbed nonlinear time-delay system but also reduce the computation time. Simulation examples are included to illustrate the procedures.