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IMA Journal of Mathematical Control and Information 1984 1(1):83-94; doi:10.1093/imamci/1.1.83
© 1984 by Institute of Mathematics and its Applications
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Lie Brackets and Singular Optimal Control

D. J. BELL

Control Systems Centre, University of Manchester Institute of Science and Technology P.O. Box 88, Manchester M60 1QD

Those branches of mathematics known as differential topology and Lie algebras have played an increasing role in practical application of control theory over the last decade. One area in which these subjects have proved useful is optimal control of dynamical systems. This paper briefly reviews the way in which the binary operation of a Lie algebra, known as a Lie bracket, has been used to obtain results for optimal control problems in which the controls can be singular.


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