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Showing 1 to 13 of 13 for “"Balanced Truncation"”.
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On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems
Balanced truncation model reduction for linear systems yields reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In …
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Reduced Order Controllers for Distributed Parameter Systems
… technique. One such model reduction technique is balanced truncation. However, it has been argued that this type of method may have an inherent weakness since there is a loss of physical information from the high order, PDE approximating model prior to control design. In an attempt to capture …
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Dimension Reduction in Structured Dynamical Systems: Optimal-𝓗<sub>2</sub> Approximation, Data-Driven Balancing, and Real-Time Monitoring
… We generalize conditions for which the balanced truncation $mathcal{H}_{infty}$ error bound is known to hold with equality. Specifically, we show that the bound is tight for single-input, single-output systems for which the truncated part of the model is a mild generalization of …
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Model Reduction for Linear Time-Varying Systems
… of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply …
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Finite Horizon Optimality and Operator Splitting in Model Reduction of Large-Scale Dynamical System
… the Iterative Rational Krylov Algorithm (IRKA), Balanced Truncation (BT), and Hankel Norm Approximation. However, these methods generally target stable systems and the approximation is performed over an infinite time horizon. If we are interested in a finite horizon reduced model, we utilize …
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An interpolation-based approach to the weighted H2 model reduction problem
… and compare it with the frequency-weighted balanced truncation method. We observe that, for virtually all of our numerical examples, the proposed method outperforms the frequency-weighted balanced truncation method.
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On Modeling and Nonlinear Model Reduction in Automotive Systems
… with a more systematic approach based on the balanced truncation method.The main contribution of this thesis is a method for model reduction of nonlinear systems. The procedure is focused on reducing the number of states using information obtained by linearization around trajectories. The …
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Dynamic-Data Driven Real-Time Identification for Electric Power Systems
… computational issues by implementing the balanced truncation method. By obtaining more realistic system models, together with timely updated parameters and stochastic influence consideration, we can have an accurate portrait of the ongoing phenomena in an electrical power system. Hence we …
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Model reduction for Hidden Markov models
… can be interpreted as an extension of the balanced truncation method to the broader class of Jump Linear Systems. In the Hidden Markov Model case, Hidden Markov Models are identified with appropriate Jump Linear Systems that satisfy certain constraints on the coefficients of the linear …
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The Search for a Reduced Order Controller: Comparison of Balanced Reduction Techniques
… approximating finite-dimensional system using a balanced reduction method known as balanced truncation and then design a control for the lower order system. The unsettling idea about this method is that it involves discarding information and then designing a control. What if valuable physical …
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Hydrologic-economic modeling of irrigated agriculture in the Lower Murrumbidgee Catchment : investigations into sustainability
… states is substantially reduced using balanced truncation, a technique used in control engineering. A simple representation of the salinization process is derived from detailed numerical simulations of unsaturated zone flow and salt transport. These detailed simulations include …
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Reduced-Order Reference Models for Adaptive Control of Space Structures
… to reduced-order modeling (in particular balanced-state and modal techniques) as applied to structural finite element models, this work produced tools for visualizing the relationship between the modes of a model and the states of its balanced representation.</p> <p>Specifically, error …
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X-ray microscope performance enhancement through control architecture change
The goal of this thesis is to apply control algorithms to improve the performance of nanopositioning devices used on the beamline in Advanced Photon Source (APS) at Argonne National Laboratory (ANL). A prototype device, better known as the Early User Instrument (EUI) was the subject of this work. …