In this study, we consider a nonsmooth optimal control problem. First, we convert this problem into the corresponding smooth optimal control problem using a practical generalized derivative. Next, we utilize the Chebyshev pseudo-spectral method to solve the smooth problem and analyze the feasibility and convergence of the approximations obtained. Finally, we approximate the optimal solutions of some nonsmooth optimal control problems.
Noori Skandari, M. H., Kamyad, A. V., & Effati, S. (2016). Smoothing approach for a class of nonsmooth optimal control problems. Applied Mathematical Modelling, 40(2), 886–903. https://doi.org/10.1016/j.apm.2015.05.014