caa a22 4500 46316914X CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10957-007-9229-6 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9229-6 Functional Optimal Estimation Problems and Their Solution by Nonlinear Approximation Schemes [Elektronische Daten] [A. Alessandri, C. Cervellera, M. Sanguineti] The design of state estimators for nonlinear dynamic systems affected by disturbances is addressed in a functional optimization framework. The estimator contains an innovation function that has to be chosen within a suitably defined class of functions in such a way to minimize a cost functional given by the worst-case ratio of the ℒ p norms of the estimation error and the disturbances. Since this entails an infinite-dimensional optimization problem that under general hypotheses cannot be solved analytically, an approximate solution is sought by minimizing the cost functional over linear combinations of simple "basis functions,” represented by computational units with adjustable parameters. The selection of the parameters is made by solving a constrained nonlinear programming problem, where the constraints are given by pointwise conditions that ensure the well-definiteness of the functional and the existence of a solution. Penalty terms are introduced in the cost function to account for constraints imposed on points that result from sampling the sets to which the trajectories of the state and of the estimation error belong. To ensure an efficient covering of the sets, low-discrepancy sampling techniques are exploited that generate samples deterministically spread in a uniform way, without leaving regions of the space undersampled. Springer Science+Business Media, LLC, 2007 Optimal estimation nationallicence Infinite-dimensional optimization nationallicence Nonlinear approximation schemes nationallicence Nonlinear programming nationallicence Low-discrepancy sequences nationallicence Alessandri A. Department of Production Engineering, Thermoenergetics, and Mathematical Models, University of Genova, Genova, Italy aut Cervellera C. Institute of Intelligent Systems for Automation, National Research Council of Italy, Genova, Italy aut Sanguineti M. Department of Communications, Computer, and System Sciences, University of Genova, Genova, Italy aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 445-466 0022-3239 134:3<445 2007 134 10957 https://doi.org/10.1007/s10957-007-9229-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9229-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alessandri A. Department of Production Engineering, Thermoenergetics, and Mathematical Models, University of Genova, Genova, Italy aut NATIONALLICENCE 700 1- Cervellera C. Institute of Intelligent Systems for Automation, National Research Council of Italy, Genova, Italy aut NATIONALLICENCE 700 1- Sanguineti M. Department of Communications, Computer, and System Sciences, University of Genova, Genova, Italy aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 445-466 0022-3239 134:3<445 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer