TIME-SUBOPTIMAL CONTROL DESIGN OF SINGULARLY PERTURBED SYSTEMS BY REDUCED-ORDER FEEDBACK DESIGN

In the paper a new method for feedback control of singularly perturbed systems (SPS) is developed; it is based on the separation of slow and fast motions. The main problems concerned with SPS are the difficulti es with high-order systems, singularly perturbed switching hypersurfac es and limit cycles. This obstacle can be alleviated by means of decou pling the slow and fast variables. The control goal is the reduction o f dimensionality. The composite control design is elaborated.The first step is the time-optimal design for the slow subsystem. The second st ep consists in a Lyapunov-type control for the fast system. The advant age is an important reduction of computational amount and a simplified implementation of the control. The disadvantage is the suboptimality but the error is in order of the small parameter a. Simulation results have shown the effectiveness of the composite algorithm, compared wit h the reduced order control. (C) 1998 IMACS/Elsevier Science B.V.