Verified Parameter Identification for Dynamic Systems with Non-Smooth Right-Hand Sides

Modeling of systems in engineering involves two major stages. First, a system structure is derived that is based on the fundamental laws from physics that characterize the relevant processes. Second, specific parameter values are determined by minimizing the distance between the measured and simulated system outputs. In previous work, strategies for verified parameter identification using techniques from interval analysis were developed. These techniques are extended in this paper to a verified estimation for systems with non-smooth ordinary differential equations. Suitable experimental results for parameter estimation of a mechanical system with friction conclude this contribution to highlight the practical applicability of the developed identification procedure.

[1]  Andreas Rauh,et al.  Experimental comparison of interval-based parameter identification procedures for uncertain ODEs with non-smooth right-hand sides , 2015, 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR).

[2]  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).

[3]  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).

[4]  Nedialko S. Nedialkov,et al.  Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques , 2011 .

[5]  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).

[6]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[7]  H. Aschemann,et al.  Interval methods for simulation of dynamical systems with state-dependent switching characteristics , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

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

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

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

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