An Eigenvalue Approach to Infinite-Horizon Optimal Control

Authors:	Rutquist Per, Volvo Technology Corporation, Sweden Breitholtz Claes, Chalmers University of Technology, Sweden Wik Torsten, Volvo Technology Corporation, Sweden
Topic:	2.4 Optimal Control
Session:	Stochastic Optimal Control
Keywords:	stochastic systems, optimal control, inventory control

Abstract

A method for finding optimal control policies for first orderstate-constrained, stochastic dynamic systems in continuous timeis presented. The method relies on solution of theHamilton-Jacobi-Bellman equation, which includes a diffusion termrelated to the stochastic disturbance in the model. A variabletransformation is applied that turns the infinite-horizon optimalcontrol problem into a linear eigenvalue problem in state-space.The method is demonstrated on a buffer control problem for a fuelcell-supercapacitor system. The obtained closed-form solutionexplains the shape of previous heuristically found control lawsfor this type of problem.