Optimal control of a rate-independent evolution equation via viscous regularization

TL;DR

This paper develops a regularization approach to derive optimality conditions for controlling a rate-independent system with non-smooth solution mappings, using viscous regularization and smoothing techniques.

Contribution

It introduces a novel regularization method combining smoothing and viscosity to analyze and derive optimality conditions for non-smooth rate-independent control problems.

Findings

Regularized problem analyzed successfully

Necessary optimality conditions derived for original problem

Viscous regularization approach effective for non-smooth systems

Abstract

We study the optimal control of a rate-independent system that is driven by a convex, quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality conditions, we study the regularization of the problem via a smoothing of the dissipation potential and via the addition of some viscosity. The resulting regularized optimal control problem is analyzed. By driving the regularization parameter to zero, we obtain a necessary optimality condition for the original, non-smooth problem.