Distributed Control: A Sequentially Semi-Separable Approach for Spatially Heterogeneous Linear Systems

Rice, Justin K.; Verhaegen, Michel

doi:10.1109/tac.2009.2019802

Cited by 60 publications

(52 citation statements)

References 69 publications

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“…However, when adding or multiplying two SSS matrices, the dimension of the subsystem interconnections v i m and v i p will be the sum of the dimensions of the subsystem interconnections of both terms. In [20] efficient order reduction techniques have been proposed to limit the dimensions of the interconnections, which can be applied after each addition or multiplication.…”

Section: B Frozen Flow As a Sequentially Semi-separable Systemmentioning

confidence: 99%

“…Efficient algorithms for addition, (matrix-vector and matrix-matrix) multiplication, and inversion have been derived that exploit the fact that the calculations can be performed on the level of the local subsystems [19]. In [20] efficient methods, based on sign iterations, have been proposed for solving Riccati equations as well. The sign iterations preserve the SSS structure, such that the solution of the Riccati equation has a SSS structure as well.…”

Section: Introductionmentioning

confidence: 99%

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Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

et al. 2010

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Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order.

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Section: B Frozen Flow As a Sequentially Semi-separable Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

et al. 2010

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“…Specifically, we consider the problem of robustness analysis of large-scale uncertain systems, which appear for instance, in applications involving discretized partial differential equations (PDEs) such as flexible structures, vehicle platooning, aircraft and satellite formation flight, (Swaroop and Hedrick, 1996;Rice and Verhaegen, 2009;Massioni and Verhaegen, 2009). Here we particularly focus on two examples of such systems, namely complex systems that include a large number of states and have large uncertainty dimensions, such as aircraft control systems, and large-scale interconnected uncertain systems.…”

Section: Introductionmentioning

confidence: 99%

“…This is mainly due to insufficient memory or processing power of available centralized work stations or in general our limited capability to solve the centralized problem in a timely manner. Such challenges are commonly addressed by exploiting structure in the problem and devising efficient solvers that use the available computational and memory resources more wisely, e.g., see Wallin et al (2009);Hansson and Vandenberghe (2000); Rice and Verhaegen (2009);Massioni and Verhaegen (2009).…”

Section: Introductionmentioning

confidence: 99%

Divide and Conquer: Distributed Optimization and Robustness Analysis

Pakazad

2015

Linköping Studies in Science and Technology. Dissertations

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Linköping 2015Cover illustration: A design approach for distributed optimization alogirhtms, used in papers C and F. It states that given the sparstiy graph of a coupled optimization problem, defined in Section 5.1, we can group its variables and its constituent subprobelms so that the coupling structure can be represented using a tree. We can then solve the problem distributedly using message passing, which utilizes the tree as its computational graph. To my parents AbstractAs control of large-scale complex systems has become more and more prevalent within control, so has the need for analyzing such controlled systems. This is particularly due to the fact that many of the control design approaches tend to neglect intricacies in such systems, e.g., uncertainties, time delays, nonlinearities, so as to simplify the design procedure. Robustness analysis techniques allow us to assess the effect of such neglected intricacies on performance and stability. Performing robustness analysis commonly requires solving an optimization problem. However, the number of variables of this optimization problem, and hence the computational time, scales badly with the dimension of the system. This limits our ability to analyze large-scale complex systems in a centralized manner. In addition, certain structural constraints, such as privacy requirements or geographical separation, can prevent us from even forming the analysis problem in a centralized manner.In this thesis, we address these issues by exploiting structures that are common in large-scale systems and/or their corresponding analysis problems. This enables us to reduce the computational cost of solving these problems both in a centralized and distributed manner. In order to facilitate distributed solutions, we employ or design tailored distributed optimization techniques. Particularly, we propose three distributed optimization algorithms for solving the analysis problem, which provide superior convergence and/or computational properties over existing algorithms. Furthermore, these algorithms can also be used for solving general loosely coupled optimization problems that appear in a variety of fields ranging from control, estimation and communication systems to supply chain management and economics.v Populärvetenskaplig sammanfattningRegulatorer för styrning av system är ofta designade med hjälp av en beskrivning, typiskt en matematisk modell, av det man vill styra. Dessa modeller är oftast endast approximativa beskrivningar av det verkliga systemet och därför behäftade med osäkerheter. Detta medför att det beteende man förväntar sig av ett reglerat system baserat på den matematiska modellen inte alltid stämmer överens med det observerade beteendet. Att analysera hur stor denna avvikelse kan bli kallas robusthetsanalys. Detta är ett väl studerat område för mindre och medelstora system. Dock är kunskaperna begränsade för riktigt stora system, speciellt om man inte vill göra en alltför konservativ analys. Exempel på stora system är kraftnät och flygplan. Kraftnät är stora på gr...

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“…Similarly, the authors in Kim and Braatz (2012) put forth a decomposable analysis approach which is applicable to interconnection of identical subsystems. An overview of distributed algorithms for analysis of systems governed by Partial Differential Equations, PDEs, is given in Rice and Verhaegen (2009b). In contrast to the above mentioned papers, in this paper, we investigate the possibility of decomposition of the analysis problem based on the sparsity in the interconnections.…”

Section: Introductionmentioning

confidence: 99%

Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems

Pakazad

Andersen

Hansson

et al. 2013

IFAC Proceedings Volumes

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Abstract:We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected uncertain systems. To facilitate distributed implementation of robust stability analysis of such systems, we describe two algorithms based on decomposition and simultaneous projections. The first algorithm is a nonlinear variant of Cimmino's mean projection algorithm, but by taking the structure of the constraints into account, we can obtain a faster rate of convergence. The second algorithm is devised by applying the alternating direction method of multipliers to a convex minimization reformulation of the convex feasibility problem. Numerical results are then used to show that both algorithms require far less iterations than the accelerated nonlinear Cimmino algorithm.

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Distributed Control: A Sequentially Semi-Separable Approach for Spatially Heterogeneous Linear Systems

Cited by 60 publications

References 69 publications

Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

Divide and Conquer: Distributed Optimization and Robustness Analysis

Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems

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