Constrained Variational Calculus for Higher Order Classical Field Theories

TL;DR

This paper introduces a geometric framework for higher order constrained field theories using a generalized Skinner-Rusk formalism, with applications to optimal control of PDEs.

Contribution

It develops an intrinsic geometric approach for higher order constrained field theories, extending classical formalisms to new applications.

Findings

Established a geometric setting for higher order constrained field theories.

Applied the framework to optimal control problems involving PDEs.

Demonstrated the utility of the formalism through specific examples.

Abstract

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular, applications to the geometrical description of optimal control theory for partial differential equations.