TIME-SCALE SYNTHESIS OF A CLOSED-LOOP DISCRETE OPTIMAL-CONTROL SYSTEM

A two-time-scale discrete control system is considered. The closed-loop optimal linear quadratic regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystem. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of an order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions.