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CivilComp Proceedings
ISSN 17593433 CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 207
Robust Performance Optimization of Linear Controlled Stochastic Systems A.A. Taflanidis^{1}, J.T. Scruggs^{2} and J.L. Beck^{3}
^{1}Department of Civil Engineering and Geological Sciences, University of Notre Dame, USA
A.A. Taflanidis, J.T. Scruggs, J.L. Beck, "Robust Performance Optimization of Linear Controlled Stochastic Systems", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 207, 2010. doi:10.4203/ccp.93.207
Keywords: robust control, probabilistic robustness, firstpassage reliability, parametric model uncertainty, stochastic simulation.
Summary
The existence of model uncertainty is important for modern control applications, as one of the main objectives is to establish optimum robustness over all possible operational conditions. Standard tools for robust control design, such as H_{infinity}, µsynthesis and the many offshoots of these, consider only compact sets of possible models for the system. Information implying that some model parameters are more probable than others is not explicitly treated. However in most real engineering applications, there is considerable knowledge about the relative plausibility of the different model parameter values. A probability logic approach provides a rational and consistent framework for quantifying this knowledge. This is established by characterizing the relative plausibility of different properties of the system by probability models. A robust design may be then established by optimizing statistics of the objective function (probabilistic performance) under the statistically described plant uncertainty, rather than the objective function resulting from the nominal model (nominal performance).
The present paper discusses the robustperformance optimization of linear time invariant dynamical systems with probabilisticallydescribed parametric model uncertainties and focuses on cases including a stochastic disturbance input. We consider H_{2} and multiobjective H_{2} control synthesis for quantification of the system nominal performance. The probabilistic measure of optimality is then defined either as the average (i.e. expectation) of the performance over the uncertain parameter space, or the probability that the performance will exceed acceptable bounds. We also examine robust stochastic design for minimal firstpassage failure probability [1], i.e. maximal reliability of the dynamic response. In this case the definition of robust performance in presence of probabilistic model uncertainties follows directly from the axioms of probability logic. Analysis and synthesis methodologies are discussed, based on recently developed stochastic simulation techniques [2]. The influence of different probability models for describing plant uncertainty is also discussed. The design approach is illustrated in a structural control application. Probabilisticallyrobust controllers are demonstrated to yield considerable different designs compared to controllers optimized using only a nominal model, or using the "worstcase" interpretation of system robustness. Also, differences are shown in the design characteristics between different probabilistic characterizations for the system uncertainty or for the performance objective. References
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