Anthony Bloch

Department of Mathematics

University of Michigan

**Stabilization by the Method of Controlled Lagrangians**

In this talk, which describes joint work with J. Marsden, N. Leonard and D. Chang, I will describe a method for the stabilization of mechanical systems using controlled Lagrangians. The key idea is that of matching, which involves finding new autonomous Lagrangian (the control Lagrangian) which produces the feedback controlled equations for the original mechanical system. The method is based on the type of Lagrangian used in the Kaluza-Klein theory for describing the motion of particle in a magnetic field. The advantage of the method is that it provides a natural Lyapunov function for analyzing stability. Various examples will be discussed, including spherical pendula and satellites. I also will describe the relationship of this work to that of Krishnaprasad, Hamburg, Auckley and others.

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