Optimal Feedback Policy for the Tracking Control of Markovian Jump Boolean Control Networks over a Finite Horizon

This paper aims to find optimal feedback policies for the tracking control of Markovian jump Boolean control networks (MJBCNs) over a finite horizon. The tracking objective is a predetermined time-varying trajectory with a finite length. To minimize the expected total tracking error between the output trajectory of MJBCN and the reference trajectory, an algorithm is proposed to determine the optimal policy for the system. Furthermore, considering the penalty for control input changes, a new objective function is obtained by weighted summing the total tracking error with the total variation of control input. Certain optimal policies sre designed using an algorithm to minimize the expectation of the new objective function. Finally, the methodology is applied to two simplified biological models to demonstrate its effectiveness.