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An algebraic framework for linear identification

Michel FliessHebertt Sira-Ramírez — 2003

ESAIM: Control, Optimisation and Calculus of Variations

A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

An algebraic framework for linear identification

Michel FliessHebertt SiraRamírez — 2010

ESAIM: Control, Optimisation and Calculus of Variations

A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

Correcteurs proportionnels-intégraux généralisés

Michel FliessRichard MarquezEmmanuel DelaleauHebertt Sira-Ramírez — 2002

ESAIM: Control, Optimisation and Calculus of Variations

Nous introduisons pour les systèmes linéaires constants les reconstructeurs intégraux et les correcteurs proportionnels-intégraux généralisés, qui permettent d’éviter le terme dérivé du PID classique et, plus généralement, les observateurs asymptotiques usuels. Notre approche, de nature essentiellement algébrique, fait appel à la théorie des modules et au calcul opérationnel de Mikusiński. Plusieurs exemples sont examinés.

Correcteurs proportionnels-intégraux généralisés

Michel FliessRichard MarquezEmmanuel DelaleauHebertt SiraRamírez — 2010

ESAIM: Control, Optimisation and Calculus of Variations

For constant linear systems we are introducing and , which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.

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