# Differential Geometry Control Theory

*Algebra/Geometry/Topology Seminar*

*by Victor Ayala*

*Institution:*Universidad Catolica del Norte

*Date: Tue 12th October 2010*

*Time: 2:00 PM*

*Location: 615 Redmond Barry, The University of Melbourne*

*Abstract*: Let G be a connected Lie group. In this talk we present the class L of linear control systems on G as introduced in [1]. We show that L contains the linear and bilinear classes of systems on Euclidean spaces and the class of invariant control systems on G. We study both controllability and optimality properties of L in some particular cases, [2] ; [3]. On the other hand, through the Morse theory we show some directions towards a topological clasiÃ‚â€¦cation of bilinear control systems, [4].

References

[1] V. Ayala, J. Tirao. Linear Control Systems on Lie Groups and Controlla- bility. American Mathematical Society, Series: Symposia in Pure Mathematics, Vol. 64, pp. 47-64, 1999.

[2] V. Ayala and L. San Martin. Controllability Properties of a Class of Control Systems on Lie Groups. Lectures Notes in Control and Information Science, Vol. 1, No. 258, pp. 83-92, 2001.

[3] V. Ayala, J. Rodriguez and L. San Martin, Optimality on homogeneous space. An example on the real projective line. SIAM Journal on Control and Optimization, 2009, 48, (4) pp. 2.636-2.650.

[4] V. Ayala, F. Colonius and W. Kliemann. On Topological Equivalence of Linear Flows with Applications to Bilinear Control Systems. Journal of Dynam- ical and Control Systems, Vol 13, No, 3, pp 313-336, 2007.

*For More Information:* contact: Craig Westerland. email: c.westerland@ms.unimelb.edu.au