Paramter Identification for PDEs
Parameter identification for systems described by partial differential equations
DFG-project "Parameteridentifikation in Systemen mit örtlich verteilten Parametern und örtlich konzentrierten Messgrößen"
Model-based control strategies require viable mathematical models describing a process to be controlled with sufficient accuracy. The parameters of these models have to be known in advance for the controller to work properly. While more often than not these parameters cannot be identified offline, thus necessitating powerful online estimation algorithms, here, the identification is further complicated by the class of systems under consideration: The parameters of systems with spatially distributed parameters described by linear partial differential equations are to be identified using only a small number of concentrated measurements, e.g. boundary values.
Where, in general, identification approaches rely on some sort of approximation of the (infinite-dimensional) distributed parameter system, the method proposed in this project does not. The project mainly aims at advancing the theorectial framework for the method as well as analyzing numerical issues involved. So far, the new identification approach has successfully been applied to numerous systems both in theory and in practice. It has also shown promise in the identification of system orders and structures, especially but not limited to systems with non-integer orders, i.e. systems of fractional order.
N. Gehring, J. Rudolph, An Algebraic Approach to the Identification of Linear Systems with Fractional Derivatives, in: 20th World Congress of the International Federation of Automatic Control (IFAC 2017) , Toulouse, France, 2017.
N. Gehring, C. Stauch, and J. Rudolph, Parameter identification, fault detection and localization for an electrical transmission line, in: Proc. European Control Conference, Aalborg, Denmark, June 29 - July 1, 2016, pp. 2090-2095, 2016. PDF
N. Gehring, J. Rudolph, An algebraic algorithm for parameter identification in a class of systems described by linear partial differential equations, PAMM - Proc. in Appl. Mathem. and Mechanics, 16, 39-42, 2016. DOI
C. Stauch, N. Gehring, and J. Rudolph, Algebraic parameter identification for infinite dimensional fluid transmission line models, Proc. IME J. Syst. Contr. Eng., 227, 732-742, 2013.
N. Gehring, T. Knüppel, J. Rudolph und F. Woittennek, Algebraische Methoden zur Parameteridentifikation für das schwere Seil, at - Automatisierungstechnik, 60, 514-521, 2012. pdf
N. Gehring, J. Rudolph, and C. Stauch, Algebraic identification of fluid parameters using transmission line dynamics, in: Proc. 13th Mechatronics Forum International Conference, Linz, Austria, September 17-19, 2012, pp. 930-935, 2012. pdf
N. Gehring, T. Knüppel, J. Rudolph, and F. Woittennek, Algebraic identification of heavy rope parameters, in: Proc. 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012, pp. 161-166, 2012.
N. Gehring, T. Knüppel, J. Rudolph, and F. Woittennek, Parameter identification for a heavy rope with internal damping, PAMM - Proc. in Appl. Mathem. and Mechanics, 12:725-726, 2012.
N. Gehring, J. Rudolph, and C. Stauch, Identification of transmission line parameters using algebraic methods, PAMM - Proc. in Appl. Mathem. and Mechanics, 12:727-728, 2012.
J. Rudolph und F. Woittennek, Ein algebraischer Zugang zur Parameteridentifikation in linearen unendlichdimensionalen Systemen, at - Automatisierungstechnik, 55, 457-467, 2007. pdf