# American Institute of Mathematical Sciences

2012, 2(3): 631-654. doi: 10.3934/naco.2012.2.631

## Perturbation feedback control: A geometric interpretation

 1 Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899 2 Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026

Received  September 2011 Revised  March 2012 Published  August 2012

Perturbation feedback control is a classical procedure in control engineering that is based on linearizing a nonlinear system around some locally optimal nominal trajectory. In the presence of terminal constraints defined by a $k$-dimensional embedded submanifold, the corresponding flow of extremals for the underlying system gives rise to a canonical foliation in the $(t,x)$-space consisting of $(n-k+1)$-dimensional leaves and $k$-dimensional cross sections. In this paper, the connections between the formal computations in the engineering literature and the geometric meaning underlying these constructions are described.
Citation: Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 631-654. doi: 10.3934/naco.2012.2.631
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