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Iterative Greedy LMI for Sparse Control

Masaaki Nagahara, Masaki Ogura, Yutaka Yamamoto
2021 IEEE Control Systems Letters  
We propose an efficient algorithm for the solution based on Dykstra's projection algorithm.  ...  This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter  ...  That is, we solve the feasibility problem with k = 12 and the LMIs in (3) with γ =γ. We adopt the ℓ 1 -optimal coefficients in Fig. 4a as the initial guess for the iterative greedy LMI algorithm.  ... 
doi:10.1109/lcsys.2021.3087964 fatcat:bap3y47tajdn3g2tl2422mqnpm

Distributed robust stability analysis of interconnected uncertain systems

Martin S. Andersen, Anders Hansson, Sina K. Pakazad, Anders Rantzer
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
This allows us to solve the analysis problem efficiently and in a distributed manner.  ...  We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.  ...  For large networks, solving the sparse LMI can be much faster, but for small and mediumsized networks, the original dense LMI (16) may be cheaper to solve. IV.  ... 
doi:10.1109/cdc.2012.6426306 dblp:conf/cdc/AndersenHPR12 fatcat:ldhwtdkevjejfmfldz5anzz5tm

Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition [article]

Sina Khoshfetrat Pakazad, Anders Hansson, Martin S. Andersen, Anders Rantzer
2014 arXiv   pre-print
The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit.  ...  Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions.  ...  The frequency-gridding-based approach solves the analysis problem approximately, by establishing the feasibility of the LMI in (4) for finite number of frequencies.  ... 
arXiv:1402.2066v1 fatcat:cxwgpz5xhnexte6w63ripggyxe

Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition

Sina Khoshfetrat Pakazad, Anders Hansson, Martin S. Andersen, Anders Rantzer
2014 IFAC Proceedings Volumes  
The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit.  ...  Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions.  ...  The frequency-gridding-based approach solves the analysis problem approximately, by establishing the feasibility of the LMI in (4) for finite number of frequencies.  ... 
doi:10.3182/20140824-6-za-1003.01649 fatcat:v4yc2bqkirby3awhgc3x2crfq4

Model reduction for linear parameter varying systems using scaled diagonal dominance

Harald Pfifer, Tamas Peni
2016 2016 American Control Conference (ACC)  
Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large scale model reduction problems more efficiently.  ...  In general, this requires the solution of a large set of linear matrix inequalities, leading to numerical issues and high computational cost.  ...  The authors would like to thank Peter Seiler for the fruitful discussions and Gary Balas for providing great support throughout the research.  ... 
doi:10.1109/acc.2016.7525344 dblp:conf/amcc/PfiferP16 fatcat:dzoediylynbs3bt7mo5lqs4zby

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

Martin S. Andersen, Sina Khoshfetrat Pakazad, Anders Hansson, Anders Rantzer
2014 IEEE Transactions on Automatic Control  
The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach  ...  We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness  ...  (13) is more efficient when the number of subsystems is large, and SMCP yields the best results for N > 70.  ... 
doi:10.1109/tac.2014.2305934 fatcat:7cvnv257l5dwfkc6hpana5rkra

A bundle method for efficiently solving large structured linear matrix inequalities

S.A. Miller, R.S. Smith
2000 Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)  
A new algorithm is proposed for solving large LMI feasibility problems, which exploits the structure of the LMI and avoids forming and manipulating large matrices.  ...  It is derived from the spectral bundle method of Helmberg and Rendl, but modified to properly handle inexact eigenvalues and eigenvectors obtained from Lanczos iterations.  ...  Acknowledgment: This work was supported by NSF grants ECS-9634498 and ECS-9978562.  ... 
doi:10.1109/acc.2000.876732 fatcat:hkev5gh3f5hxzli32ezwzblkda

Chordal sparsity, decomposing SDPs and the Lyapunov equation

Richard P. Mason, Antonis Papachristodoulou
2014 2014 American Control Conference  
For large LMIs it is important to exploit structure and sparsity within the problem in order to solve the associated Semidefinite Programs efficiently.  ...  In this paper we decompose SDPs by taking advantage of chordal sparsity, and apply our method to the problem of constructing Lyapunov functions for linear systems.  ...  INTRODUCTION Many problems in control theory can be formulated as Linear Matrix Inequalities (LMIs) and solved using convex optimisation algorithms [1] , [2] .  ... 
doi:10.1109/acc.2014.6859255 dblp:conf/amcc/MasonP14 fatcat:46ew4rp4dfdhbemntnhs3o2csm

Sparsity-Promoting Sensor Selection for Non-Linear Measurement Models

Sundeep Prabhakar Chepuri, Geert Leus
2015 IEEE Transactions on Signal Processing  
We also propose a projected subgradient algorithm that is attractive for large-scale problems. The developed theory is applied to sensor placement for localization.  ...  We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. The proposed solvers result in sparse sensing techniques.  ...  To handle large-scale problems, we have also presented a projected subgradient algorithm.  ... 
doi:10.1109/tsp.2014.2379662 fatcat:a7kqo6yrjbf4lorhzlexwc6sum

Set-Membership Error-in-Variables Identification Through Convex Relaxation Techniques

V. Cerone, D. Piga, D. Regruto
2012 IEEE Transactions on Automatic Control  
A new approach for the computation of parameter uncertainty intervals is presented. First, the identification problem is formulated in terms of nonconvex optimization.  ...  In this paper the set membership error-in-variables identification problem is considered, that is the identification of linear dynamic systems when both output and input measurements are corrupted by bounded  ...  to medium and large scale problems.  ... 
doi:10.1109/tac.2011.2168073 fatcat:ndt2z7zqunghpbzerwnhddaac4

Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design [article]

Soodeh Habibi and Arefeh Kavand and Michal Kocvara and Michael Stingl
2021 arXiv   pre-print
The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions.  ...  We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient preconditioner fully utilizing the low-rank information.  ...  They present a preconditioner for the CG method within a standard IP method that makes it more efficient for large-and-sparse low-rank SDPs.  ... 
arXiv:2105.08529v1 fatcat:lfs7lhj32zc3piphkbfn2cthza

Linear matrix inequalities with chordal sparsity patterns and applications to robust quadratic optimization

Martin S. Andersen, Lieven Vandenberghe, Joachim Dahl
2010 2010 IEEE International Symposium on Computer-Aided Control System Design  
The algorithms take advantage of fast recursive algorithms for evaluating the function values and derivatives for the logarithmic barrier functions of the cone of positive semidefinite matrices with a  ...  We discuss nonsymmetric interior-point methods for linear cone programs with chordal sparse matrix cone constraints.  ...  Chordal Matrix Algorithms A number of sparse matrix problems can be solved efficiently by specialized algorithms when the underlying sparsity pattern is chordal.  ... 
doi:10.1109/cacsd.2010.5612788 dblp:conf/cacsd/AndersenVD10 fatcat:effa7wzdynenvd6ljrc5jmvl3u

Hybrid system identification: An SDP approach

C. Feng, C. M. Lagoa, N. Ozay, M. Sznaier
2010 49th IEEE Conference on Decision and Control (CDC)  
Moreover, to address computational complexity issues, an equivalent rank minimization problem subject to deterministic LMI constraints is provided, as efficient convex relaxations for rank minimization  ...  Namely, by recasting the identification problem as polynomial optimization, we develop deterministic algorithms, in which the inherent sparse structure is exploited.  ...  Conversely, if Problem 3 has a feasible solution m, and if rank M N (m, I k ) = rank M Ni (m, I k ) for all k and rank M N (m, I k ∩ I j ) = 1 for all pairs (j, k) with I k ∩ I j = ∅, then, V s (r, e)  ... 
doi:10.1109/cdc.2010.5718082 dblp:conf/cdc/FengLOS10 fatcat:cea5flsolzckbik6qlidjbzhya

Low-rank solutions of matrix inequalities with applications to polynomial optimization and matrix completion problems

Ramtin Madani, Ghazal Fazelnia, Somayeh Sojoudi, Javad Lavaei
2014 53rd IEEE Conference on Decision and Control  
This paper is concerned with the problem of finding a low-rank solution of an arbitrary sparse linear matrix inequality (LMI). To this end, we map the sparsity of the LMI problem into a graph.  ...  The results of this work can be readily applied to three separate problems of minimumrank matrix completion, conic relaxation for polynomial optimization, and affine rank minimization.  ...  feasible solution X of the above problem, its associated submatrix W is feasible for (7) and satisfies rank{W} ≤ rank{X}.  ... 
doi:10.1109/cdc.2014.7040064 dblp:conf/cdc/MadaniFSL14 fatcat:muahfrpfijcb5aasa7rzghcn2a

Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems* *This research is supported by the Swedish department of education within the ELLIIT research program

Sina Khoshfetrat Pakazad, Martin S. Andersen, Anders Hansson, Anders Rantzer
2013 IFAC Proceedings Volumes  
These problems arise in robust stability analysis of large, weakly interconnected uncertain systems.  ...  We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled.  ...  We refer to this algorithm as Algorithm 2. Feasibility Detection For strictly feasible problems, algorithms 1 and 2 converge to a feasible solution.  ... 
doi:10.3182/20130708-3-cn-2036.00008 fatcat:u5u6ldm4kvbplcouuqscihcpdm
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