Abstract
This paper discusses optimal and suboptimal control policies which transfer second-order systems to the origin while minimizing some function of control effort <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f_{0}^{T}\phi[u(t)]dt</tex> . The time of control <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> is specified only to the extent <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T\leq\bar{T}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{T}</tex> is the given upper bound on control time. Control systems with unequal negative real poles are considered. A computational scheme which yields the optimal control policies for these systems is developed, and suboptimal policies are then derived. The effects of suboptimal policies on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f_{0}^{T}\phi[u(t)]dt</tex> are also evaluated.
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