Abstract

The stochastic logical control dynamical system with finite state is considered. After giving two equivalent descriptions of stochastic logical dynamical system: in term of discrete-time evolution equation and in term of Markov process, the infinite horizon optimization problem is presented in an algebraic form. Based on semi-tensor product of matrix and the increasing dimensional technique, we establish a succinct matrix expression of dynamic programming and Bellman's equation for the optimal control problem.

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