Relaxation methods for optimal control problems

Abstract

We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map $A:{\mathbb{R}}^N\to 2^{{\mathbb{R}}^N}$. We do not assume that $D(A)={\mathbb{R}}^N$, incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.

References in corpus (4)

• Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions
• Nonlinear elliptic inclusions with unilateral constraint and dependence on the gradient
• Nonlinear second order evolution inclusions with noncoercive viscosity term
• Periodic solutions for implicit evolution inclusions