Measure Valued Directional Sparsity for Parabolic Optimal Control Problems

Measure Valued Directional Sparsity for Parabolic Optimal Control Problems

A directional sparsity framework allowing for measure valued controls in the spatial direction is proposed for parabolic optimal control problems. It allows for controls which are localized in space, where the spatial support is independent of time. Well-posedness of the optimal control problems is established and the optimality system is derived. It is used to establish structural properties o...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Directional Sparsity in Optimal Control of Partial Differential Equations

We study optimal control problems in which controls with certain sparsity patterns are preferred. For time-dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval. The approach uses a nondifferentiable cost functional to implement the sparsity requirements; additionally, bound constraints...

A New Optimal Solution Concept for Fuzzy Optimal Control Problems

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...