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Scheduling of a limited communication channel for optimal control

We outline a method for optimal offline scheduling of a limited bandwidth communication channel that is used for control purposes. We study LQ-control of parallel control processes and describe how the theory for periodic control can be used for defining a cost functional that measures the performances of sampled data systems in relation to desired continuous time performances. This formulation results in a complex combinatorial optimization problem which is solved by exhaustive search and the solution can be viewed as an optimal allocation of the limited communication resources. The resulting optimal sequences are typically such that the sampling is nonuniform, but the control law is time varying and computed to take this nonuniform sampling into account. In an example, two inverted pendulums with different closed loop performances that share a common communication resource are studied. The resulting optimal sequences are in agreement with the intuitive idea that the sampling resources should be focused to where they are needed the most, that is, to the controller with the fastest closed loop characteristics.