Stochastic minimum-energy control

TL;DR

This paper presents a solution to the minimum-energy control problem for linear stochastic systems, optimizing control energy via a Hamiltonian-type stochastic differential equation.

Contribution

It introduces a novel approach to solve the minimum-energy control problem using forward-backward stochastic differential equations for linear systems.

Findings

Provides explicit solution for minimum-energy control in stochastic systems.

Connects control problem to Hamiltonian-type stochastic differential equations.

Enhances understanding of energy-efficient control strategies in stochastic dynamics.

Abstract

We give the solution to the minimum-energy control problem for linear stochastic systems. The problem is as follows: given an exactly controllable system, find the control process with the minimum expected energy that transfers the system from a given initial state to a desired final state. The solution is found in terms of a certain forward-backward stochastic differential equation of Hamiltonian type.