A Computational Framework for Optimal Control Using Polynomial-Based Approximation Methods with Applications in Intelligent Systems

Abstract

This work suggests an approximate direct technique to treat special kind of optimal control problem (OCP) in the finite domain [0, T] based on new modified family of Vieta-Pell functions. The proposed method employs a direct parameterization approach. In such technique, we approximate the state variables in terms modified family of Vieta-Pell functions and then transform the original optimal control problem to a constrained nonlinear programming problem. The aim of the presented algorithm is to reduce the numerical complexity with computational efficiency. The algorithm is well-suited for implementation in scientific computing environments such as MATLAB and Python, making it applicable to software-based control systems. To demonstrate its practical relevance to information technology applications, the proposed method is applied to optimal control problems arising in intelligent robotic systems, particularly robotic arm motion planning. Numerical simulations confirm fast convergence, high accuracy, and robustness, making the method suitable for integration into digital control architectures, intelligent automation systems, and IT-based robotic platforms.