Optimal control for reachability of Markov jump switching Boolean control networks subject to output trackability

Abstract

This article aims at designing the finite horizon optimal control sequence (FHOCS) for ensuring the reachability of Markov jump switching Boolean control networks (MJSBCNs) subject to output trackability. The key step in solving such a problem is to construct a Luenberger-like observer (LLO). Our approach includes a few steps as follows. We firstly propose the formulation of the optimal control problem (OCP) of maximising the probability of finite-time reachability subject to output trackability. Then, by converting the dynamics of MJSBCNs into an equivalent expectation system, an LLO is established for MJSBCNs. In this setup, a Luenberger-like observation matrix is constructed, which is an effect tool to solve the finite-time reachability problem. Finally, an LLO method is developed to find the FHOCS by maximising the T -step Luenberger-like observation matrix. In a biological example, we show the effectiveness of our developed methods.