Approximating with Lipschitz Controls Original Research Article

For nonlinear nonconvex control systems in finite dimensional state spaces we approximate measurable controls by Lipschitz controls. We give explicit approximation rates. It turns out that the corresponding trajectories converge uniformly on bounded time intervals and that the approximation is of order O(M−1/2), as M→∞, where M>0 is the Lipschitz constant of the Lipschitz controls.