Solving discrete first-order matrix linear control problems with general parametric uncertainties: A probability-density-based approach

Abstract

This paper deals with the probabilistic analysis of discrete first-order linear control models with uncertainties. For the sake of generality in our stochastic analysis, we assume that all model parameters (the initial and final states, the matrix containing the free dynamics part, and the control’s coefficient) are random variables with an arbitrary joint probability density function. We then combine some results from classical Control Theory with Probability Theory to obtain, under very general hypotheses, the first probability density function of the control and the solution, which are parametric stochastic processes. To illustrate our theoretical findings, we also show two numerical examples and a classical discrete macroeconomic model whose parameters are treated as random variables.