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This article addresses the observer design problem for simultaneous state and parameter estimation for a class of one-dimensional linear parabolic PDEs. The design is based on the backstepping PDE methodology, including a modified integral transformation to compensate for the parameter uncertainty. The solution of the resulting Kernel-PDE is recast as a convex optimization problem via a Sum-of-Squares...
Connections between function approximation and classes of functional optimization problems, whose admissible solutions may depend on a large number of variables, are investigated. The insights obtained in this context are exploited to analyze families of nonlinear approximation schemes containing tunable parameters and enjoying the following property: when they are used to approximate the (unknown)...
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