A non-autonomous stochastic discrete time system with uniform disturbances

TL;DR

This paper develops Bayesian optimal control strategies for non-autonomous linear stochastic discrete-time systems with uniform disturbances, extending previous work to generalized systems with non-square matrices and singular cases.

Contribution

It introduces Bayesian control solutions for systems with uniform disturbances, including singular cases and generalized systems with non-square matrices, expanding prior exponential family results.

Findings

Bayesian control is obtained via solving linear algebraic equations.

Optimization techniques are used for singular linear systems.

Results extend to generalized systems with non-square coefficient matrices.

Abstract

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors 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. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family.