Time-suboptimal control design of singularly perturbed systems by reduced order feedback design Original Research Article

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 difficulties with high-order systems, singularly perturbed switching hypersurfaces and limit cycles. This obstacle can be alleviated by means of decoupling the slow and fast variables. The control goal is the reduction of dimensionality. The composite control design is elaborated. The first step is the time-optimal design for the slow subsystem. The second step consists in a Lyapunov-type control for the fast system. The advantage 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 ε. Simulation results have shown the effectiveness of the composite algorithm, compared with the reduced order control.