Desensitized Optimal Control

Abstract

Desensitized optimal control (DOC) enables the formulation of optimal control problems that incorporate the optimal reference solution’s sensitivities to state perturbations into the optimization process. Mathematically, this is achieved through the introduction of Lagrange multiplierlike quantities that act as additional state variables and capture the desired sensitivity information. By penalizing user-specified sensitivities, the reference solution becomes easier to control under feedback. Thus, the DOC method can be viewed as a method to improve nonlinear robustness. By converting fixed parameters appearing in the problem formulation to state variables with trivial dynamics, the DOC approach can be used to improve robustness to parameter uncertainties. The paper also analyzes the relationship between sensitivities and the covariance matrix and compares the benefits and limitations of covariance shaping versus DOC. A simple Zermelo-type boat path optimization problem with uncertainties in the water current is analyzed to demonstrate the DOC approach.