Approximate solution of a class of singular control problems |
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Authors: | R. B. Vinter |
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Affiliation: | (1) Decision and Control Sciences Group, Electronics Systems Laboratory, Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts |
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Abstract: | A class of singular control problems involving amplitude constraints on the controls is examined. IfL is the space of control functionsU, the control constraint setS can be identified with the unit ball inL. Now, for anyn (1, ), an analogous problem may be set up withLn forU and the unit ball inLn forS. This modified problem is necessarily nonsingular for controllable systems. It is shown that, by takingn sufficiently large, the solution to the modified problem also solves the original problem arbitrarily closely (in a sense made precise). Behavior asn is investigated.This research was supported by the Science Research Council of Great Britain and the Commonwealth Fund (Harkness Fellowship). |
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Keywords: | Duality theory linear systems nonlinear programming convex programming distributed control systems |
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