Controllability of nilpotent systems

• Autorzy: Victor Ayala Bravo
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the controllability property of invariant control systems on Lie groups. In [1], the authors state: ``If there exists a real function strictly increasing on the positive trajectories, then the system cannot be controllable". To develop this idea, the authors define the concept of symplectic vector via the co-adjoint representation. We are interested in finding algebraic conditions to determine the existence of symplectic vectors in nilpotent Lie algebras. In particular, we state a necessary and sufficient condition for controllability in the simply connected nilpotent case.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 32
• Numer: 1
• Strony: 35-46

Daty

wydano

1995

Twórcy

autor

Victor Ayala Bravo

• Departamento de Matemática, Universidad Católica del Norte Casilla, 1280, Antofagasta, Chile

Bibliografia

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• [2] B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of invariant vector fields on the semidirect product of Lie groups, Trans. Amer. Math. Soc. 271 (1982), 521-535.
• [3] R. Brockett, Systems theory on group manifolds and coset spaces, SIAM J. Control 10 (1972), 265-284.
• [4] L. Corwin and F. Greenleaf, Representations of Nilpotent Lie Groups and Their Applications, Part I, Cambridge University Press, 1990.
• [5] V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179.
• [6] V. Jurdjevic and H. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313-329.
• [7] I. Kupka, Introduction to the Theory of Systems, 16 Coloquio Brasileiro de Matematica, 1987.
• [8] L. San Martin and P. Crouch, Controllability on principal fibre bundle with compact structure group, Systems Control Letters 5 (1984), 35-40.
• [9] H. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188.