Technology of logical synthesis of periodic trajectory in a controlled Boolean network

Abstract

A technology for automating structural-parametric synthesis of a Boolean network with a given periodic trajectory is proposed. This technology provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. The proposed technology is based on the author's method of Boolean restrictions. According to this method, all conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. A software implementation of the proposed technology using microservice-oriented tools is presented. All stages of the parametric synthesis of a Boolean network in accordance with the proposed technology are demonstrated in the example of a one-step linear system.