Design of Optimal Controls in Acausal LQG Problems

TL;DR

This paper explores the design of optimal controls for acausal linear-quadratic-Gaussian (LQG) problems, extending control theory to systems where outputs depend on future inputs, a less-studied area.

Contribution

It systematizes existing results on acausal systems and provides a foundational background for designing optimal controls in acausal LQG problems.

Findings

Provides a structured overview of acausal control systems

Establishes a theoretical framework for acausal LQG control design

Bridges gap between causal and acausal control theory

Abstract

In control theory, a system which has output depending only on the present and past values of the input is said to be causal (or nonanticipative). Respectively, a system is acausal (or non-causal) if its output depends on future inputs as well. Overall majority of literature in stochastic control theory discusses causal systems. Only a few sources indirectly concern acausal systems. In this paper, we systemize these results under main idea of acausality and present a background for designing optimal controls in acausal LQG problems.