Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

Andreas Rauh; Johanna Minisini; Eberhard P. Hofer

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 3, page 425-439
  • ISSN: 1641-876X

Abstract

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Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.

How to cite

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Andreas Rauh, Johanna Minisini, and Eberhard P. Hofer. "Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 425-439. <http://eudml.org/doc/207946>.

@article{AndreasRauh2009,
abstract = {Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.},
author = {Andreas Rauh, Johanna Minisini, Eberhard P. Hofer},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interval arithmetic; reachability analysis; observability analysis; robust stability; model-based design of optimal controllers},
language = {eng},
number = {3},
pages = {425-439},
title = {Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties},
url = {http://eudml.org/doc/207946},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Andreas Rauh
AU - Johanna Minisini
AU - Eberhard P. Hofer
TI - Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 3
SP - 425
EP - 439
AB - Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
LA - eng
KW - interval arithmetic; reachability analysis; observability analysis; robust stability; model-based design of optimal controllers
UR - http://eudml.org/doc/207946
ER -

References

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