Smoothing approach for a class of nonsmooth optimal control problems

•Proposal of a practical generalized derivative for nonsmooth functions.•Conversion of nonsmooth optimal control problems into the smooth form.•Chebyshev pseudo-spectral method is used to solve the smooth problem.•Analysis of the feasibility and convergence of the optimal solutions obtained.•Solution of nonsmooth optimal control problems using the proposed approach.

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.