Approximation of risk-averse optimal feedback control

TL;DR

This paper develops a new iterative method for constructing feedback control laws that optimize risk-averse objectives in PDE systems with random coefficients, ensuring quadratic convergence and providing the first rigorous synthesis for such problems.

Contribution

It introduces a sequential quadratic programming scheme for risk-averse PDE control, achieving local quadratic convergence and pioneering rigorous feedback synthesis for these complex systems.

Findings

Method converges quadratically to optimal control

First rigorous feedback synthesis for risk-averse PDE control

Effective handling of random coefficients in PDEs

Abstract

The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear entropic risk measure. A sequential quadratic programming scheme is derived that iteratively solves linear quadratic subproblems obtained through second-order Taylor expansions of the objective functional, with each subproblem re-centered at the previous iterate. It is shown that this method converges locally quadratically to the unique risk-averse optimal control. This work provides the first rigorous feedback synthesis for risk-averse objectives subject to PDEs with random coefficients.