IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2023-06-05T09:06:52ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2013-09-17T08:11:59Z2013-09-17T08:11:59Zhttp://eprints.imtlucca.it/id/eprint/1754This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/17542013-09-17T08:11:59ZComputationally Efficient Approximation Schemes for Functional OptimizationAngelo AlessandriGiorgio Gneccogiorgio.gnecco@imtlucca.itMarcello Sanguineti2013-09-13T10:33:43Z2013-09-16T12:03:00Zhttp://eprints.imtlucca.it/id/eprint/1716This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/17162013-09-13T10:33:43ZMinimizing Sequences for a Family of Functional Optimal Estimation ProblemsRates of convergence are derived for approximate solutions to optimization problems associated with the design of state estimators for nonlinear dynamic systems. Such problems consist in minimizing the functional given by the worst-case ratio between the ℒ p -norm of the estimation error and the sum of the ℒ p -norms of the disturbances acting on the dynamic system. The state estimator depends on an innovation function, which is searched for as a minimizer of the functional over a subset of a suitably-defined functional space. In general, no closed-form solutions are available for these optimization problems. Following the approach proposed in (Optim. Theory Appl. 134:445–466, 2007), suboptimal solutions are searched for over linear combinations of basis functions containing some parameters to be optimized. The accuracies of such suboptimal solutions are estimated in terms of the number of basis functions. The estimates hold for families of approximators used in applications, such as splines of suitable orders.Angelo AlessandriGiorgio Gneccogiorgio.gnecco@imtlucca.itMarcello Sanguineti2013-09-12T10:45:37Z2013-09-16T12:03:00Zhttp://eprints.imtlucca.it/id/eprint/1693This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/16932013-09-12T10:45:37ZComputationally Efficient Approximation Schemes for Functional OptimizationApproximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions
are considered, expressed as linear combinations of n-tuples from a basis set. The uses of fixed-basis and variable-basis approximation are compared. In the latter,
simple computational units with adjustable parameters are exploited. Conditions are discussed, under which the number n of basis functions required to guarantee a desired accuracy does not grow “fast” with the number d of variables in admissible solutions, thus mitigating the “curse of dimensionality”. As an example of application,
an optimization-based approach to fault diagnosis for nonlinear stochastic systems is presented. Numerical results for a complex instance of the fault-diagnosis problem are given. Angelo AlessandriGiorgio Gneccogiorgio.gnecco@imtlucca.itMarcello Sanguineti