On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

TL;DR

This paper develops a receding horizon control method for discrete-time jump linear systems with probabilistic constraints, transforming the problem into a deterministic one using inverse CDF, and demonstrates its application on a macroeconomic model.

Contribution

It introduces a novel receding horizon control framework for state-dependent jump linear systems with probabilistic constraints, utilizing inverse CDF for tractability.

Findings

Ensures mean square boundedness of the system states.

Transforms probabilistic constraints into deterministic constraints.

Successfully applied to a macroeconomic system example.

Abstract

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.