Univariate Theory of Functional Connections Applied to Component Constraints

This work presents a methodology to derive analytical functionals, with embedded linear constraints among the components of vector (e.g., coordinates) that is function single variable time). prepares background necessary for indirect solution optimal control problems via application Pontryagin Maximum Principle. The presented part univariate Theory Functional Connections has been developed solve constrained optimization problems. To increase clarity and practical aspects proposed method, mostly examples applications rather than rigorous mathematical definitions proofs.