Matches in SemOpenAlex for { <https://semopenalex.org/work/W3216324761> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W3216324761 endingPage "882" @default.
- W3216324761 startingPage "835" @default.
- W3216324761 abstract "When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L∩M and the smallest differential field (L,M ) ⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring D = K [d1,...,dn] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define L∩M and L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called Bäcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system R = homK (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject." @default.
- W3216324761 created "2021-12-06" @default.
- W3216324761 creator A5072898949 @default.
- W3216324761 date "2021-01-01" @default.
- W3216324761 modified "2023-10-01" @default.
- W3216324761 title "Differential Correspondences and Control Theory" @default.
- W3216324761 doi "https://doi.org/10.4236/apm.2021.1111056" @default.
- W3216324761 hasPublicationYear "2021" @default.
- W3216324761 type Work @default.
- W3216324761 sameAs 3216324761 @default.
- W3216324761 citedByCount "2" @default.
- W3216324761 countsByYear W32163247612022 @default.
- W3216324761 crossrefType "journal-article" @default.
- W3216324761 hasAuthorship W3216324761A5072898949 @default.
- W3216324761 hasBestOaLocation W32163247611 @default.
- W3216324761 hasConcept C10138342 @default.
- W3216324761 hasConcept C118615104 @default.
- W3216324761 hasConcept C121332964 @default.
- W3216324761 hasConcept C127413603 @default.
- W3216324761 hasConcept C134306372 @default.
- W3216324761 hasConcept C136119220 @default.
- W3216324761 hasConcept C139080492 @default.
- W3216324761 hasConcept C146978453 @default.
- W3216324761 hasConcept C162324750 @default.
- W3216324761 hasConcept C182306322 @default.
- W3216324761 hasConcept C186219872 @default.
- W3216324761 hasConcept C202444582 @default.
- W3216324761 hasConcept C202887219 @default.
- W3216324761 hasConcept C28826006 @default.
- W3216324761 hasConcept C33923547 @default.
- W3216324761 hasConcept C48209547 @default.
- W3216324761 hasConcept C51544822 @default.
- W3216324761 hasConcept C62520636 @default.
- W3216324761 hasConcept C74902906 @default.
- W3216324761 hasConcept C78045399 @default.
- W3216324761 hasConcept C93226319 @default.
- W3216324761 hasConcept C9652623 @default.
- W3216324761 hasConcept C97145343 @default.
- W3216324761 hasConceptScore W3216324761C10138342 @default.
- W3216324761 hasConceptScore W3216324761C118615104 @default.
- W3216324761 hasConceptScore W3216324761C121332964 @default.
- W3216324761 hasConceptScore W3216324761C127413603 @default.
- W3216324761 hasConceptScore W3216324761C134306372 @default.
- W3216324761 hasConceptScore W3216324761C136119220 @default.
- W3216324761 hasConceptScore W3216324761C139080492 @default.
- W3216324761 hasConceptScore W3216324761C146978453 @default.
- W3216324761 hasConceptScore W3216324761C162324750 @default.
- W3216324761 hasConceptScore W3216324761C182306322 @default.
- W3216324761 hasConceptScore W3216324761C186219872 @default.
- W3216324761 hasConceptScore W3216324761C202444582 @default.
- W3216324761 hasConceptScore W3216324761C202887219 @default.
- W3216324761 hasConceptScore W3216324761C28826006 @default.
- W3216324761 hasConceptScore W3216324761C33923547 @default.
- W3216324761 hasConceptScore W3216324761C48209547 @default.
- W3216324761 hasConceptScore W3216324761C51544822 @default.
- W3216324761 hasConceptScore W3216324761C62520636 @default.
- W3216324761 hasConceptScore W3216324761C74902906 @default.
- W3216324761 hasConceptScore W3216324761C78045399 @default.
- W3216324761 hasConceptScore W3216324761C93226319 @default.
- W3216324761 hasConceptScore W3216324761C9652623 @default.
- W3216324761 hasConceptScore W3216324761C97145343 @default.
- W3216324761 hasIssue "11" @default.
- W3216324761 hasLocation W32163247611 @default.
- W3216324761 hasLocation W32163247612 @default.
- W3216324761 hasOpenAccess W3216324761 @default.
- W3216324761 hasPrimaryLocation W32163247611 @default.
- W3216324761 hasRelatedWork W1831300786 @default.
- W3216324761 hasRelatedWork W1978997600 @default.
- W3216324761 hasRelatedWork W2010432767 @default.
- W3216324761 hasRelatedWork W2060392792 @default.
- W3216324761 hasRelatedWork W2077851858 @default.
- W3216324761 hasRelatedWork W2080895223 @default.
- W3216324761 hasRelatedWork W2377416945 @default.
- W3216324761 hasRelatedWork W2601325352 @default.
- W3216324761 hasRelatedWork W2950272280 @default.
- W3216324761 hasRelatedWork W3130490049 @default.
- W3216324761 hasVolume "11" @default.
- W3216324761 isParatext "false" @default.
- W3216324761 isRetracted "false" @default.
- W3216324761 magId "3216324761" @default.
- W3216324761 workType "article" @default.