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Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamical systems with uncertainties. (English) Zbl 1217.93057

Fitt, Alistair D. (ed.) et al., Progress in industrial mathematics at ECMI 2008. Proceedings of the 15th European conference on mathematics for industry, London, UK, June 30 - July 4, 2008. Berlin: Springer (ISBN 978-3-642-12109-8/hbk; 978-3-642-12110-4/ebook). Mathematics in Industry 15, 549-555 (2010).
Summary: Controllers for nonlinear dynamical systems are often based on properties such as differential flatness or exact input-output as well as input-to-state linearizability. However, these approaches are limited to specific classes of system models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for validated simulation of both ordinary differential equations and differential-algebraic equations is extended to the synthesis and sensitivity analysis of open-loop and closed-loop controllers. Furthermore, interval arithmetic routines for evaluation of criteria for reachability and observability of states are implemented using automatic differentiation.
For the entire collection see [Zbl 1197.00055].

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
93B50 Synthesis problems
37N35 Dynamical systems in control
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