Limited-Complexity Polyhedric Tracking
When the errors between the data and model outputs are affine in the parameter vector θ, the set of all values of θ such that these errors fall within known prior bounds is a polytope (under some identiflability conditions, which can be described exactly and recursively. However, this polytope may turn out to be too complicated for its intended use. In this chapter, an algorithm is presented for recursively computing a limited-complexity approximation guaranteed to contain the exact polytope. Complexity is measured by the number of supporting hyperplanes. The simplest polyhedric description that can thus be obtained is in the form of a simplex, but polyhedra with more faces can be considered as well. A polyhedric algorithm is also described for tracking time-varying parameters, which can accommodate both smooth and infrequent abrupt variations of the parameters. Both algorithms are combined to yield a limited-complexity polyhedric tracker.
KeywordsAdjacent Vertex Expansion Factor Convex Polyhedron Supporting Hyperplane Expansion Policy
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