Average Optimal Control of Uncertain Control-Affine Systems

TL;DR

This paper develops a framework for optimal control of uncertain control-affine systems, deriving necessary conditions and feedback controls for both known and uncertain initial conditions using an extended Pontryagin Maximum Principle.

Contribution

It introduces a Hilbert space formulation for average optimal control of uncertain systems, extending classical optimality conditions to probabilistic parameter uncertainties.

Findings

Derived necessary optimality conditions for uncertain control systems.

Characterized feedback controls for control-affine systems under uncertainty.

Extended Pontryagin Maximum Principle to infinite-dimensional spaces.

Abstract

This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, this kind of problem is crucial when parameter uncertainty matters. We derive necessary optimality conditions and characterize feedback controls for control-affine systems. Two scenarios are examined: known initial conditions (finite-dimensional case) and uncertain initial conditions (infinite-dimensional framework). The Pontryagin Maximum Principle is extended using a Hilbert space formulation.