We consider the time-optimal control problem to the origin for a class of nonlinear systems, called dual-to-linear systems. We obtain the general description of possible optimal controls. In particular, we show that optimal controls take the values −1, 0, and +1 only and have a finite number of points of discontinuity. We describe a class of nonlinear affine control systems which can be approximated by dual-to-linear systems in the sense of time optimality.
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