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A general theorem on local controllability. (English) Zbl 0629.93012
The author proves a sufficient condition of small-time local controllability of a nonlinear control system at an equilibrium point. The system considered is a C control system affine with respect to the control. Input symmetries of the system and degree of the elements of the Lie algebra generated by the system are defined. If all the brackets with certain symmetries evaluated at the equilibrium point are linear combination of brackets of lower degree, then the equilibrium point is small-time locally controllable.
Many known sufficient conditions of small-time local controllability are contained in this theorem as particular cases.
Reviewer: R.Bianchini

MSC:
93B05 Controllability
93B25 Algebraic methods
93C10 Nonlinear systems in control theory
17B99 Lie algebras and Lie superalgebras
49K15 Optimality conditions for problems involving ordinary differential equations
93B03 Attainable sets, reachability
93C15 Control/observation systems governed by ordinary differential equations
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