On the Specification Complexity of Linguistic Control Procedures
Egerstedt, Magnus B.
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In this paper we combine the ideas of trigger based hybrid systems with that of motion description languages in order to show how continuous machines should interpret and operate on computer generated symbolic (linguistic) inputs in order to make the input alphabet meaningful from a control theoretic point of view. We furthermore focus our attention on so called quantized input-output machines, i.e. machines where the admissible control signals, U, as well as the measurement set, Y, are both finite, which allows us to define a complexity measure of a given task as the minimum number of bits needed to code a word over the input alphabet that achieves the task. We also show how this measure can help us understand why feedback control is to prefer over purely open-loop control in some specific situations in terms of the specification complexity.