Intrinsic Separation Principles

TL;DR

This paper introduces an intrinsic separation principle for constrained linear systems, enabling the decomposition of dual control problems into information minimization and robust control, facilitating finite-dimensional convex optimization solutions.

Contribution

It proposes a novel information-theoretic framework that extends the classical separation theorem to systems with constraints, bridging dual control and convex optimization.

Findings

Theoretical development of an intrinsic separation principle.

Framework for approximating dual control problems via convex optimization.

Potential for application with modern polytopic computing methods.

Abstract

This paper is about output-feedback control problems for general linear systems in the presence of given state-, control-, disturbance-, and measurement error constraints. Because the traditional separation theorem in stochastic control is inapplicable to such constrained systems, a novel information-theoretic framework is proposed. It leads to an intrinsic separation principle that can be used to break the dual control problem for constrained linear systems into a meta-learning problem that minimizes an intrinsic information measure and a robust control problem that minimizes an extrinsic risk measure. The theoretical results in this paper can be applied in combination with modern polytopic computing methods in order to approximate a large class of dual control problems by finite-dimensional convex optimization problems.