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Theory and Applications of Functional Interpolation to Optimization and Control

Daniele Mortari, Texas A&M University

Roberto Furfaro, University of Arizona

Functional Interpolation is a generalization of interpolation, deriving functionals representing all functions satisfying a set of constraints. The constraints can be on values, derivatives, and integrals, and on any linear combination of them in univariate or multivariate dimensional problems. Inequality constraints are special constraints of interest. Applications of Functional Interpolation are found on solving differential (ODEs and PDEs) and integro-differential equations, on optimal control problems, on continuation methods and, in general, in constrained optimization.