Lie Theory and Control Systems Defined on Spheres | Zendy

R. Brockett | Zendy

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Lie Theory and Control Systems Defined on Spheres

Author(s) -

R. Brockett

Publication year - 1973

Publication title -

siam journal on applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.954

H-Index - 99

eISSN - 1095-712X

pISSN - 0036-1399

DOI - 10.1137/0125025

Subject(s) - controllability , mathematics , class (philosophy) , spheres , lie group , space (punctuation) , vector space , computer science , pure mathematics , physics , artificial intelligence , astronomy , operating system

We show in this paper that in constructing a theory for the most elementary class of control problems defined on spheres, some results from Lie theory play a natural role. In particular to understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is probably the most natural departure from the usual linear system/vector space problems which have dominated the control systems literature. For this reason our results are compared with those previously available for the finite-dimensional vector space case.

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