Parameter Estimation in Linear Descriptor Systems

Sammanfattning: Lineardescriptorsystems form the natural way in which linear models ofphysicalsystems are delivered from an object-oriented modeling toollikeModelica. Linear descriptor systems are also known aslineardifferential-algebraic equations in the continuous-time case.Ifsome parameters in such models are unknown, one might needtoestimate them from measured data from the modeled system. This isaform of system identification called gray box identification.Theobjective of this work is to examine how gray boxidentificationcan be performed for linear descriptor systems. Tosolve thisproblem, we use some well-known canonical forms toexamine how totransform the descriptor systems into state-spaceform. In general,the input must be redefined to make thetransformation intostate-space form possible. To be able toimplement the suggestedidentification methods, we examine how thetransformations can becomputed using numerical software from thelinear algebra packageLAPACK. Noise modeling is an importantpart of parameterestimation and system identification, so we alsoexamine how anoise model can be added to linear descriptor systems.The resultis that white noise in general cannot be added to allequations ofa linear continuous-time descriptor system, since thiscould leadto differentiation of the noise which is not welldefined. It isalso noted that a Kalman filter can be implemented ifthe model istransformed into state-space form. We also discussthe problemof finding initial values for the parameter search. Weshow how toformulate a biquadratic polynomial, that gives initialvalues forthe parameter search when minimized.