Adaptive identification of linear time-delay systems

Y. Orlov (1) , L. Belkoura (2) , Jean-Pierre Richard (2, 3) , Michel Dambrine (4)

1 CICESE - Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico]
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 Centrale Lille
4 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

Synthesis of an adaptive parameter identifier is developed for linear dynamic systems with finitely many lumped delays in the state vector and control input. These systems are governed by linear functional differential equations with uncertain time‐invariant parameters and delays. The state of the system is assumed to be available for measurements. Constructive necessary and sufficient conditions for the system parameters and delays to be identifiable are provided. Once the parameter identifiability is guaranteed the simultaneous on‐line identification of the system parameters and delays is achieved by the adaptive identifier proposed. Theoretical results are supported by numerical simulation.

Domaines: Automatique; Mathématiques [math]; Systèmes dynamiques [math.DS]; Sciences de l'ingénieur [physics]; Automatique / Robotique

Y. Orlov, L. Belkoura, Jean-Pierre Richard, Michel Dambrine. Adaptive identification of linear time-delay systems. International Journal of Robust and Nonlinear Control, 2003, 13 (9), pp.857-872. ⟨10.1002/rnc.850⟩. ⟨hal-02560771⟩