Optimal control of systems with resource constraints

In this paper optimal control of systems with constrained computation and communication resources is studied. The timing of real-time scheduling algorithms like rate monotonic scheduling and earliest deadline first scheduling is analyzed. It is shown that these scheduling algorithms lead to periodically varying sampling periods and time delays. Modeling of the resulting periodically time-varying systems is described and based on this, the design of a periodic linear quadratic regulator is presented. Applying the lifting technique, a time-invariant reformulation of the design problem is obtained. The regulator gains result from solving algebraic Riccati equations. To further improve control performance, a method which combines offline-scheduling and periodic control is proposed. The methods are illustrated by an example.