Experimental comparison of interval-based parameter identification procedures for uncertain ODEs with non-smooth right-hand sides

Interval methods provide a means to implement strategies for simulation and parameter identification of dynamic system models with bounded uncertainty. The focus of this paper is the verified identification of continuous-time dynamic systems which are characterized by ordinary differential equations with non-smooth right-hand sides. Such models arise, for example, while modeling mechanical systems with a transition between different model states such as sliding and static friction. A novel interval subdivision procedure is presented for the verified identification of such system models. A comparison of numerical results for the identification of a drive train test rig concludes this contribution and highlights the advantages in comparison to previous work.

[1]  Nedialko S. Nedialkov,et al.  Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint propagation techniques , 2009, ADHS.

[2]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[3]  Andreas Rauh,et al.  Interval Methods for Control-Oriented Modeling of the Thermal Behavior of High-Temperature Fuel Cell Stacks , 2012 .

[4]  A. Rauh,et al.  Applications of Interval Algorithms in Engineering , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).

[5]  Andreas Rauh,et al.  Verified Parameter Identification for Dynamic Systems with Non-Smooth Right-Hand Sides , 2014, SCAN.

[6]  N.S. Nedialkov,et al.  Rigorous simulation of hybrid dynamic systems with symbolic and interval methods , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[7]  Andreas Rauh,et al.  A verified method for solving piecewise smooth initial value problems , 2013, Int. J. Appl. Math. Comput. Sci..

[8]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[9]  Andreas Rauh,et al.  Reduction of overestimation in interval arithmetic simulation of biological wastewater treatment processes , 2007 .

[10]  N. Nedialkov,et al.  Interval Tools for ODEs and DAEs , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).