Vector optimal control problem on a differentiable manifold: A realistic approach

Abstract

The present paper discusses vector optimal control of a functional whose domain of definition is a product manifold M × N, where M is a differentiable manifold of dimension M and N is a differentiable manifold of dimension N with differentiable variety as its boundary respectively; N can be viewed as a set of control parameters. It also gives a new concept viz. vector valued semi optimal control of a functional on the said restricted domain. Finally, the paper establishes some examples in favour of such type of optimal control problem.