Averaged optimal control problems of non-linear differential inclusions on the finite and infinite intervals

In this paper, we use the averaging method to find an approximate solution for the optimal control of nonlinear differential inclusions with rapidly oscillating coefficients. This work highlights the interplay between averaging methods and asymptotic analysis, suggesting that a hybrid approach can provide reliable strategies for solving complex optimal control problems. Addressing both finite interval and unbounded domains, the studies together contribute to a more complete framework for understanding and applying control methodology in nonlinear settings. We use the averaging method to find an approximate solution to these optimal control problems. Future research can benefit from integrating insights from both methodologies to further improve control strategies, potentially leading to improved results in various fields of engineering and applied mathematics. The Carathéodory-type differential switching optimal control problems are considered.