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Perturbation feedback control: A geometric interpretation

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  • 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.
    Mathematics Subject Classification: Primary: 49K15, 49L99; Secondary: 93C10.


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