Control System on Boolean Networks through Semi Tensor Product Approach and Boolean Calculus

TL;DR

This paper introduces a novel control approach for Boolean networks using semi tensor product and Boolean calculus, incorporating derivatives to influence state evolution, and discusses controllability and optimal control.

Contribution

It presents a new method that integrates derivatives into Boolean control networks via semi tensor product, enhancing control analysis capabilities.

Findings

New derivative-based influence on Boolean network states

Controllability analysis with example

Discussion on optimal control significance

Abstract

We have considered a Boolean control network where the state evolution equations depend on past states, controls and first derivatives of a function with respect to controls. Total approach has been the efficient use of matrix semi tensor product and logical operators and logical equations. We have obtained a absolutely new result in considering the derivative terms to play a role to influence the states. We have discussed about controllability with an example and also optimal control and its significance in control theory.