A Sub-Ordinary Approach to Achieve Near-Exact Solutions for a Class of Optimal Control Problems

This paper explores the advantages of Sub-ODE strategy in deriving near-exact‎ ‎solutions for a class of linear and nonlinear optimal control‎ ‎problems (OCPs) that can be transformed into nonlinear‎ ‎partial differential equations (PDEs). Recognizing that converting an OCP into differential‎ ‎equations typically increases the complexity by adding constraints‎, ‎we adopt the‎ ‎Sub-ODE method‎, ‎as a direct method‎, thereby negating the need for such transformations to extract near exact solutions‎. A key advantage of this method is its ability to produce control and state functions that closely resemble the explicit forms of optimal control and state functions. ‎ We present results that demonstrate the efficacy of this method through several numerical examples, comparing its performance to various other approaches, thereby illustrating its capability to achieve near-exact solutions.