Optimal Control of Boolean Control Networks with Linear Temporal Logic Constraints

This paper addresses the optimal control problem of Boolean Control Networks under Linear Temporal Logic constraints. An algebraic framework based on the semi-tensor product approach is introduced to represent the product automata, enabling the formal verification and control of Boolean control networks with respect to LTL specifications. Two greedy algorithms are proposed: one for finite-horizon optimal control and another for infinite-horizon control, with the latter focusing on identifying optimal cycles. The efficiency of the proposed methods is demonstrated through two case studies, highlighting their potential for precise control in complex biological systems, such as gene regulatory networks.