Time-optimal control of a third order regulator
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The time-optimal control law as a function of the states for second and third-order linear regulators with real eigenvalues was derived. Notions of a switching curve for the second-order system and switching surface for the third-order system was introduced. A set of states was found which divided the state space into two distinct regions, in one of which the time-optimal control was +1 and in the other of which the time-optimal control was -1. Time-optimal control, Switching curves and surfaces, Linear time-optimal regulator.
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