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.