Title :
An information theoretic approach to model reduction based on frequency-domain Cross-Gramian information
Author :
Jinbao Fu ; Chongliang Zhong ; Yalin Ding ; Jiufei Zhou
Author_Institution :
Changchun Inst. of Opt., Fine Mech. & Phys., Chinese Acad. of Sci., Changchun, China
Abstract :
We focused our attention on model reduction for linear time invariant (LTI) continuous time systems with single input and single output (SISO). We analyzed the strongpoint and shortcoming of an information theoretic approach called minimum information loss method for model reduction. We explained relationships between the steady-state information entropy and controllability information for the Gaussian systems. The controllability, observability and Cross-Gramian information were analyzed in the time-domain. The frequency-domain Cross-Gramian information (FCGI) was defined based on Cross-Gramian matrix containing information associated with both controllability and observability. Furthermore, a valuable application of the frequency-domain Cross-Gramian information to model reduction (FCGMIL) was developed by using the concept and properties of frequency-domain Cross-Gramian information. The performance index of FCGMIL is to minimize the frequency-domain Cross-Gramian information loss caused by eliminating the state variables with weak contributions to Cross-Gramian information over some frequency band. Two numerical examples are illustrated to verify the efficiency of FCGMIL.
Keywords :
Gaussian processes; continuous time systems; controllability; linear systems; minimum entropy methods; nonlinear dynamical systems; observability; performance index; time-frequency analysis; Cross-Gramian matrix; FCGMIL; Gaussian systems; continuous time system; controllability; frequency-domain Cross-Gramian information; information theoretic approach; linear time invariant system; minimum information loss method; model reduction; observability; performance index; single input and single output; steady-state information entropy; time-domain analysis; Controllability; Eigenvalues and eigenfunctions; Frequency domain analysis; Observability; Reduced order systems; Steady-state; Time domain analysis; Controllability; Frequency-domain; Gramian; Minimum information; Model reduction; Observability;
Conference_Titel :
Intelligent Control and Automation (WCICA), 2010 8th World Congress on
Conference_Location :
Jinan
Print_ISBN :
978-1-4244-6712-9
DOI :
10.1109/WCICA.2010.5553913