Analysis and Control of Partially Observed Discrete-Event Systems via Positively Constructed Formulas

Analysis and Control of Partially Observed Discrete-Event Systems via Positively Constructed Formulas

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This paper establishes a connection between control theory for partially observed discrete-event systems (DESs) and automated theorem proving (ATP) in the calculus of positively constructed formulas (PCFs).The language of whole wheat phyllo dough PCFs is a complete first-order language providing a powerful tool for qualitative analysis of dynamical systems.Based on ATP in the PCF calculus, a new technique is suggested for checking observability as a property of formal languages, which is necessary for the existence of supervisory control of DESs.In the case of violation of observability, words causing a conflict can also be extracted with the help of a specially designed PCF.With an example of the problem of path planning by a robot in an unknown environment, we show the application of our viqua-f4 approach at one of the levels of a robot control system.

The prover Bootfrost developed to facilitate PCF refutation is also presented.The tests show positive results and perspectives for the presented approach.