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The correspondence between minimum-energy control of linear systems with arbitrary functional constraints on the output and spline interpolation is examined. It is shown that the spline that interpolates the given constraints is the output of the given system when driven by the optimal control. This fact yields a simple general formula for the minimum-energy control. A duality result for minimum-energy...
We show here how fast estimation algorithms can be obtained by developing innovations decompositions that exploit certain shift-invariance properties of the involved processes. Such invariances are quite natural for stationary processes and can be employed through the use of backwards innovations processes to develop a set of identities for the solutions of the associated Wiener-Hopf equations. These...
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