Optimal on-line scheduling of multiple control tasks: a case study

We study the problem of dynamically scheduling a set of state-feedback control tasks controlling a set of linear plants. We consider an on-line non-preemptive scheduling policy that is optimal in the sense that it minimizes a quadratic performance criterion for the overall system. The optimal scheduling decision at each point in time is a function of the states of the controlled plants. To be able to solve the scheduling problem for realistic examples, we use the technique of relaxed dynamic programming to compute suboptimal solutions with error bounds. The approach is compared to earlier approaches in a case study involving simultaneous control of one ball-and-beam process and two DC-servo processes. We also show how the scheduling policy can be modified to allow for background tasks to execute when the need for control is small