A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE

TL;DR

This paper introduces a numerical model reduction method for optimal control of systems with multiple time scales, avoiding the need for explicit singular perturbation form, and demonstrates its advantages and limitations through examples.

Contribution

It proposes a novel numerical scheme for optimal control problems with time scale separation that does not require explicit singular perturbation formulation.

Findings

Effective in handling systems with multiple time scales

Demonstrates advantages over traditional methods

Identifies limitations through example analysis

Abstract

Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is based on a model reduction approach that does not need the system to be explicitly stated in singularly perturbed form. We present examples that highlight the advantages and disadvantages of the method.