An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems

This paper investigates the finite horizon optimal control problem for the stochastic logical dynamical systems with finite states. After giving the equivalent descriptions of stochastic logical dynamical system in term of Markov process, the finite horizon optimization problem is presented in an algebraic form. Based on semi-tensor product of matrix and the increasing dimensional technique, a succinct algebraic expression of dynamic programming algorithm is derived to solve the optimal control problem. Examples, including an application on stochastic Kleene's logical optimization problem, are presented to show the effectiveness of our main result.