Design of least costly identification experiments. The main philosophy accompanied by illustrative examples

The goal of this paper is on the one hand to give a tutorial on the main ideas of a recently introduced paradigm for optimal experiment design whose objective is to design the least costly identification experiment while guaranteeing a sufficiently accurate model for e.g. control. On the other hand, the second goal is to illustrate with well chosen examples the advantages of designing optimally the excitation signal for an identification instead of using a classical white excitation. As we will see in these examples, shaping appropriately the excitation signal allows one to reduce significantly the cost of an identification experiment.

[1]  Håkan Hjalmarsson,et al.  Input design via LMIs admitting frequency-wise model specifications in confidence regions , 2005, IEEE Transactions on Automatic Control.

[2]  Håkan Hjalmarsson,et al.  Identification for robust H2 deconvolution filtering , 2010, Autom..

[3]  Håkan Hjalmarsson,et al.  Identification for control of multivariable systems: Controller validation and experiment design via LMIs , 2008, Autom..

[4]  Ioan Doré Landau,et al.  A Flexible Transmission System as a Benchmark for Robust Digital Control , 1995, Eur. J. Control.

[5]  K. Lindqvist.  On Experiment Design in Identification of Smooth Linear Systems , 2001 .

[6]  Jay H. Lee.  Control-Relevant Experiment Design for Multivariable Systems , 1997 .

[7]  Martin B. Zarrop,et al.  Optimal experiment design for dynamic system identification , 1977 .

[8]  Lennart Ljung,et al.  Optimal experiment designs with respect to the intended model application , 1986, Autom..

[9]  Roland Hildebrand,et al.  Identification for control: optimal input design with respect to a worst-case /spl nu/-gap cost function , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  Lennart Ljung,et al.  Some results on optimal experiment design , 2000, Autom..

[11]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[12]  Håkan Hjalmarsson,et al.  System identification of complex and structured systems , 2009, 2009 European Control Conference (ECC).

[13]  X. Bombois,et al.  Cheapest open-loop identification for control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  V. Fromion,et al.  Computation of the robustness margin with the skewed m tool , 1997 .

[15]  H. Hjalmarsson,et al.  Optimal Input Design Using Linear Matrix Inequalities , 2000 .

[16]  Vincent Fromion,et al.  H ∞ control for a flexible transmission system , 1997 .

[17]  Håkan Hjalmarsson,et al.  Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design , 2009, Autom..

[18]  Håkan Hjalmarsson,et al.  For model-based control design, closed-loop identification gives better performance , 1996, Autom..

[19]  Xavier Bombois,et al.  Least costly identification experiment for control , 2006, Autom..

[20]  X. Bombois,et al.  Least costly identification experiment for control. A solution based on a high-order model approximation , 2004, Proceedings of the 2004 American Control Conference.

[21]  Marion Gilson,et al.  Cheapest identification experiment with guaranteed accuracy in the presence of undermodeling , 2006 .

[22]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .