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

Abstract

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 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 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.