Approximate predictability of Pseudo-Metric Systems
Autor: | Gabriella Fiore, Giordano Pola, Maria Domenica Di Benedetto, Elena De Santis |
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Jazyk: | angličtina |
Rok vydání: | 2020 |
Předmět: |
0209 industrial biotechnology
Class (set theory) Current (mathematics) Basis (linear algebra) Relation (database) Computer science Approximate simulation 02 engineering and technology Computer Science Applications Approximate predictability 020901 industrial engineering & automation Piecewise affine systems Pseudo–metric systems Symbolic models Control and Systems Engineering Hybrid system 0202 electrical engineering electronic engineering information engineering Applied mathematics 020201 artificial intelligence & image processing Metric system Predictability Finite set Analysis |
Popis: | In this paper, we introduce and characterize the notion of approximate predictability for the general class of pseudo-metric systems, which are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems. Approximate predictability corresponds to the possibility of predicting the occurrence of specific states belonging to a particular subset of interest, in advance with respect to their occurrence, on the basis of observations. We establish a relation between approximate predictability of a given pseudo-metric system and approximate predictability of a pseudo-metric system that approximately simulates the given one. This relation allows checking approximate predictability of a system with an infinite number of states, provided that one is able to construct a pseudo-metric system with a finite number of states and inputs, approximating the original one in the sense of approximate simulation. To demonstrate the usefulness of our results, we apply them to the analysis of approximate predictability of Piecewise Affine (PWA) systems, a well studied class of hybrid systems for which, however, to the best of our knowledge, there are no results available in the current literature on predictability. An illustrative example is also included, which demonstrates the applicability of our results. |
Databáze: | OpenAIRE |
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