On infinite dimensional linear programming approach to stochastic control

TL;DR

This paper explores the infinite dimensional linear programming approach to stochastic control, specifically for linear quadratic Gaussian systems, revealing connections to Riccati LMIs and multi-objective criteria.

Contribution

It establishes a link between inf-LP methods and Riccati LMIs for LQG problems, and relates multi-objective and chance constraints to inf-LP.

Findings

Derivation of Riccati LMIs from inf-LP for LQG.

Connection between multi-objective criteria and inf-LP.

Insight into computational intractability of inf-LP in general.

Abstract

We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By focusing on linear systems with quadratic cost (LQG), we establish a connection between this approach and the well-known Riccati LMIs. In particular, we show that the semidefinite programs known for the LQG problem can be derived from the pair of primal and dual inf-LPs. Furthermore, we establish a connection between multi-objective and chance constraint criteria and the inf-LP formulation.