Bayesian optimal control for a non-autonomous stochastic discrete time system

The main objective of this article is to develop Bayesian optimal control for a class of non‐autonomous linear stochastic discrete time systems. By taking into consideration that the disturbances in the system are given by a random vector with components belonging to an exponential family with a natural parameter, we prove that the Bayes control is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. Furthermore, we extend these results to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of this type of systems are non‐square matrices.