C-DOC: Co-State Desensitized Optimal Control

TL;DR

This paper introduces C-DOC, a novel optimal control framework that uses co-states to reduce sensitivity of the optimal cost to parameter variations, enhancing robustness.

Contribution

The paper develops a new method that incorporates co-states into the control problem to desensitize the cost function against parameter uncertainties.

Findings

Reduces cost dispersion due to parametric variations

Establishes relationship between co-states and cost-to-go function

Demonstrates effectiveness through numerical examples

Abstract

In this paper, co-states are used to develop a framework that desensitizes the optimal cost. A general formulation for an optimal control problem with fixed final time is considered. The proposed scheme involves elevating the parameters of interest into states, and further augmenting the co-state equations of the optimal control problem to the dynamical model. A running cost that penalizes the co-states of the targeted parameters is then added to the original cost function. The solution obtained by minimizing the augmented cost yields a control which reduces the dispersion of the original cost with respect to parametric variations. The relationship between co-states and the cost-to-go function, for any given control law, is established substantiating the approach. Numerical examples and Monte-Carlo simulations that demonstrate the proposed scheme are discussed.