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Towards a multiresolution approach to linear control

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1 Author(s)
Girard, A. ; VERIMAG, Gieres

We develop a multiresolution approximation framework for linear control. We construct a multiresolution analysis of the set of input functions of a linear system. The approximation of an input u at a scale j is defined as the input uj of minimal energy such that the trajectories of the system associated with u and uj coincide on a grid of step length 2-j. We propose a set of wavelet functions which generate this multiresolution analysis. These functions, called control theoretic wavelets, satisfy useful properties for the representation of control inputs of a linear system. As an example of application of our multiresolution approximation framework, we propose a method for efficient encoding of control inputs with regard to several criteria

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Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 8 )