Stochastic Control Systems

Abstract

The concept of a stochastic control system is defined as a map from a tuple of the current state and the current input to the conditional probability distribution of the tuple of the next state and the current output. A Gaussian stochastic control system representation is defined which represents such a stochastic system. Stochastic controllability is defined as the property that there exists an input trajectory such that the probability distribution of a future state equals a prespecified particular probability distribution. A characterization of stochastic controllability of a Gaussian stochastic control system is provided.