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Control of a class of nonsmooth dynamical systems

In this paper, the authors propose an approach to control a class of nonsmooth continuous and discontinuous dynamical systems which is based on a generalization of derivative and Chebyshev pseudospectral (PS) methods. First a generalized derivative for nonsmooth functions, which is proposed by Kamyad et al. is considered. Therefore the obtained generalized derivative of a nonsmooth function is approximated with the Fourier series. So, the nonsmooth control problem is approximated by a smooth optimal control problem and in what follows, it is solved by Chebyshev PS method and the approximate solution for the state and control of the main problem is achieved. Finally, some numerical examples of the control of nonsmooth dynamical systems are solved to illustrate the efficiency of the authors’ approach.