An Analytical Approach to Quadratic Optimal Control Problems Governed by Higher-Order Ordinary Differential Equations

• Author(s): Ayodeji Sunday Afolabi
• Paper ID: 1711824
• Page: 2666-2676
• Published Date: 08-12-2025
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 5 November-2025

Abstract

This research presents a comprehensive analytical framework for solving quadratic optimal control problems (OCPs) governed by higher-order ordinary differential equations (ODEs). The core methodology involves transforming the higher-order system into an equivalent first-order system through state variable expansion, thereby enabling the direct application of Pontryagin’s Maximum Principle. This transformation facilitates the derivation of the necessary conditions for optimality, leading to a coupled system of state and costate equations. The general solution to this two-point boundary value problem is constructed analytically, utilizing matrix exponentials and eigenpair expansions for linear systems with constant coe?icients. The e?icacy of the analytical approach is demonstrated through detailed solutions to illustrative examples involving second-order ODE constraints. The results con- firm the method’s ability to yield explicit expressions for the optimal state, control, and adjoint trajectories, establishing it as a robust and systematic analytical tool for this important class of OCPs.

Keywords

Optimal Control, Higher-Order Odes, Pontryagin’s Principle, Analytical Solutions, Adjoint Equations

Citations

IRE Journals:
Ayodeji Sunday Afolabi "An Analytical Approach to Quadratic Optimal Control Problems Governed by Higher-Order Ordinary Differential Equations" Iconic Research And Engineering Journals Volume 9 Issue 5 2025 Page 2666-2676

IEEE:
Ayodeji Sunday Afolabi "An Analytical Approach to Quadratic Optimal Control Problems Governed by Higher-Order Ordinary Differential Equations" Iconic Research And Engineering Journals, 9(5)