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Optimal approximation rates for Lipschitz controls

For nonlinear nonconvex control systems we investigate the approximation properties of Lipschitz controls. In case that the control range is connected, any trajectory produced by a measurable control can be approximated by trajectories produced by Lipschitz controls. The approximation is of order O(M/sup -1/2/), where M is the Lipschitz constant. An example shows that this approximation order is optimal.