A comparative study of chaotic map strategies for solving optimal control problems

This study presents a comparative numerical analysis of four chaotic map-based strategies for solving Optimal Control Problems (OCPs). The proposed framework involves a two-phase process: first, OCPs are discretized and reformulated as nonlinear optimization problems; subsequently, optimization is performed using the Logistic Chaotic Reduction (LCR), Improved Logistic Chaotic Reduction (ILCR), Logistic Chaotic Reduction with Gradient Search, and Chaotic Gradient-based Optimization (CGO) algorithms. To evaluate performance, five benchmark problems are examined. Among the methods tested, CGO demonstrates superior convergence speed and solution precision. Numerical results show that integrating chaotic dynamics with gradient-based search effectively balances exploration and exploitation, mitigates premature convergence, and improves numerical accuracy. A comparative analysis with conventional techniques across multiple test cases further confirms the computational efficiency and robustness of CGO. These findings position chaotic optimization as a viable and competitive alternative to traditional gradient-based and heuristic approaches in solving OCPs.

کلیدواژه ها:

Optimal control problems ، Numerical optimization methods ، Chaos Theory ، Chaotic Maps