Abstract
The dual mode optimal control problem to find a control u to minimize J= 1 2 ∫ 0 ∞ x′Qx dt subject to the constraints Q > 0, x ̇ = Fx + gu , ¦u¦ ⩽ 1, is solved for its “singular” solutions using well known quadratic regulator theory. The significance of the approach, apart from any due to its simplicity, is that it may be readily extended to handle cases when Q is positive semidefinite. It is also quite straightforward to extend the results to the time-varying multiple-input case.
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