THEORY OF CONNECTIONS APPLIED TO FIRST-ORDER SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS SUBJECT TO COMPONENT CONSTRAINTS

2018 Univelt Inc. All rights reserved. Motivated by a class of first order differential equations generated by some optimal control problems this paper provides, using the methodology introduced by the Theory of Connections, least-squares solutions of first-order differential equations systems subject to linear constraints on the vectors components. This paper solves all different cases occurring in 22 linear time-varying systems with forcing term. Then, it shows how to solve a 4 4 system generated by a simple optimal control problem and how to solve a generic 33 time-varying differential equation system subject to relative and integral constraints on the vector components.

THEORY OF CONNECTIONS APPLIED TO FIRST-ORDER SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS SUBJECT TO COMPONENT CONSTRAINTS Conference Paper