Continuity and Monotonicity Properties of an Optimally Controlled Double Integrator with State and Input Constraints
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Purwin, Oliver; D'Andrea, Raffaello
This paper presents minimum-time solutions for driving a double integrator to a desired state with zero final velocity. The presence of constraints on the magnitude of the control input and the velocity state is assumed. The derived solutions are piecewise constant control efforts, which have to be executed in sequence. Finally, it is shown that the required times are strictly monotone and continuous functions of the constraints.
computer science; technical report
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