A novel numerical method for solving optimal control problems using fourth-degree hat functions

Abstract

This paper focuses on solving a class of nonlinear optimal control problems by constructing novel hat functions based on fourth-order polynomials, namely, fourth-degree hat functions (FDHFs). The FDHFs are used in this method to approximate the state equations and cost function. In fact, the FDHFs enable us to turn the optimal control problem under consideration into a nonlinear optimal control problem with unknown coefficients that is easy to solve by any numerical method. The main advantages of the proposed method are its simplicity, ease of application, low computational expense, and avoidance of numerical integration. Several examples have been discussed to demonstrate the efficacy and applicability of the suggested method.

Keywords

• Fourth-degree hat functions
• Nonlinear optimal control
• Operational matrix
• Computational method