Singular optimal controls for second-order saturating systems

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Abstract
The synthesis of optimal controls for second-order linear systems with a saturable scalar input is considered. A non-quadratic cost functional is introduced which, as in the case of quadratic cost, can give rise to singular solutions ; the associated optimal controls are explicitly characterized and, in contrast to the case of quadratic cost, act over a finite time interval only. For a double integrator system it is shown that, under certain conditions, the optimal control is identical to the minimum-time solution.