Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
multi-agent system; $H_{\infty }$ norm; network robustness; adaptive interpolation
multi-agent system; $H_{\infty }$ norm; network robustness; adaptive interpolation
Summary:
We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the $H_{\infty }$ norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient $H_{\infty }$ norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the $H_{\infty }$ norm.
References:
[1] Aliyev, N., Benner, P., Mengi, E., Schwerdtner, P., Voigt, M.: A greedy subspace method for computing the $\mathcal{L}_\infty$-norm. PAMM, Proc. Appl. Math. Mech. 17 (2017), 751-752. DOI 10.1002/pamm.201710343
[2] Aliyev, N., Benner, P., Mengi, E., Schwerdtner, P., Voigt, M.: Large-scale computation of $\mathcal{L}_\infty$-norms by a greedy subspace method. SIAM J. Matrix Anal. Appl. 38 (2017), 1496-1516. DOI 10.1137/16M1086200 | MR 3735291 | Zbl 1379.65020
[3] Antoulas, A. C.: Approximation of Large-Scale Dynamical Systems. Advances in Design and Control 6. SIAM, Philadelphia (2005). DOI 10.1137/1.9780898718713 | MR 2155615 | Zbl 1112.93002
[4] Antoulas, A. C., Beattie, C. A., Gugercin, S.: Interpolatory model reduction of large-scale dynamical systems. Efficient Modeling and Control of Large-Scale Systems Springer, New York (2010), 3-58. DOI 10.1007/978-1-4419-5757-3_1 | MR 0593759 | Zbl 1229.65103
[5] Antoulas, A. C., Beattie, C. A., Güğercin, S.: Interpolatory Methods for Model Reduction. Computational Science & Engineering 21. SIAM, Philadelphia (2020). DOI 10.1137/1.9781611976083 | MR 4072177 | Zbl 1553.93002
[6] Antoulas, A. C., Sorensen, D. C., Gugercin, S.: A survey of model reduction methods for large-scale systems. Structured Matrices in Mathematics, Computer Science, and Engineering. I Contemporary Mathematcs 280. AMS, Providence (2001), 193-219. DOI 10.1090/conm/280 | MR 1850408 | Zbl 1048.93014
[7] Baur, U., Beattie, C. A., Benner, P., Gugercin, S.: Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33 (2011), 2489-2518. DOI 10.1137/090776925 | MR 2861634 | Zbl 1254.93032
[8] Beattie, C., Gugercin, S.: Interpolatory projection methods for structure-preserving model reduction. Syst. Control Lett. 58 (2009), 225-232. DOI 10.1016/j.sysconle.2008.10.016 | MR 2494198 | Zbl 1159.93317
[9] Benner, P., Breiten, T., Damm, T.: Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems. Int. J. Control 84 (2011), 1398-1407. DOI 10.1080/00207179.2011.601761 | MR 2830869 | Zbl 1230.93010
[10] Benner, P., Gugercin, S., Willcox, K.: A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev. 57 (2015), 483-531. DOI 10.1137/130932715 | MR 3419868 | Zbl 1339.37089
[11] Benner, P., Kürschner, P., Tomljanović, Z., Truhar, N.: Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm. ZAMM, Z. Angew. Math. Mech. 96 (2016), 604-619. DOI 10.1002/zamm.201400158 | MR 3502967 | Zbl 1538.74119
[12] Benner, P., Mehrmann, V., (eds.), D. C. Sorensen: Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering 45. Springer, Berlin (2005). DOI 10.1007/3-540-27909-1 | MR 2516498 | Zbl 1066.65004
[13] Benner, P., Sima, V., Voigt, M.: $\mathcal{L}_\infty$-norm computation for continuous-time descriptor systems using structured matrix pencils. IEEE Trans. Automat. Control 57 (2012), 233-238. DOI 10.1109/TAC.2011.2161833 | MR 2917665 | Zbl 1369.93174
[14] Boyd, S., Balakrishnan, V.: A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its {$\mathcal{L}_{\infty}$}-norm. Syst. Control Lett. 15 (1990), 1-7. DOI 10.1016/0167-6911(90)90037-U | MR 1065342 | Zbl 0704.93014
[15] Bruinsma, N. A., Steinbuch, M.: A fast algorithm to compute the $H_{\infty}$-norm of a transfer function matrix. Syst. Control Lett. 14 (1990), 287-293. DOI 10.1016/0167-6911(90)90049-Z | MR 1052637 | Zbl 0699.93021
[16] Dileep, G.: A survey on smart grid technologies and applications. Renewable Energy 146 (2020), 2589-2625. DOI 10.1016/j.renene.2019.08.092
[17] Gallivan, K., Vandendorpe, A., Dooren, P. Van: Model reduction of MIMO systems via tangential interpolation. SIAM J. Matrix Anal. Appl. 26 (2004), 328-349. DOI 10.1137/S0895479803423925 | MR 2124150 | Zbl 1078.41016
[18] Gugercin, S., Antoulas, A. C., Beattie, C.: $\mathcal{H}_2$ model reduction for large-scale linear dynamical systems. SIAM J. Matrix Anal. Appl. 30 (2008), 609-638. DOI 10.1137/060666123 | MR 2421462 | Zbl 1159.93318
[19] Haddad, W. M., Hui, Q., Lee, J.: Network Information Systems: A Dynamical Systems Approach. Other Titles in Applied Mathematics 191. SIAM, Philadelphia (2023). DOI 10.1137/1.9781611977547 | MR 4625045 | Zbl 1520.93002
[20] Hagberg, A. A., Schult, D. A., Swart, P. J.: Exploring network structure, dynamics, and function using networkX. Proceedings of the 7th Python in Science Conference (SciPy2008) SciPy, Pasadena (2008), 11-16.
[21] Leinhardt, S.: Social Networks: A Developing Paradigm. Academic Press, New York (1977). DOI 10.1016/C2013-0-11063-X
[22] Nakić, I., Tolić, D., Palunko, I., Tomljanović, Z.: Numerically efficient agents-to-group $H_{\infty}$ analysis. IFAC-PapersOnLine 55 (2022), 199-204. DOI 10.1016/j.ifacol.2022.09.095
[23] Nakić, I., Tolić, D., Tomljanović, Z., Palunko, I.: Numerically efficient ${H}_{\infty}$ analysis of cooperative multi-agent systems. J. Franklin Inst. 359 (2022), 9110-9128. DOI 10.1016/j.jfranklin.2022.09.013 | MR 4498292 | Zbl 1501.93012
[24] Olfati-Saber, R., Murray, R. M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49 (2004), 1520-1533. DOI 10.1109/TAC.2004.834113 | MR 2086916 | Zbl 1365.93301
[25] Peng, S., Zhou, Y., Cao, L., Yu, S., Niu, J., Jia, W.: Influence analysis in social networks: A survey. J. Network Comput. Appl. 106 (2018), 17-32. DOI 10.1016/j.jnca.2018.01.005
[26] Ren, W., Beard, R. W.: Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Communications and Control Engineering. Springer, London (2008). DOI 10.1007/978-1-84800-015-5 | Zbl 1144.93002
[27] Rommes, J., Martins, N.: Efficient computation of transfer function dominant poles using subspace acceleration. IEEE Trans. Power Syst. 21 (2006), 1218-1226. DOI 10.1109/TPWRS.2006.876671
[28] Rommes, J., Sleijpen, G. L. G.: Convergence of the dominant pole algorithm and Rayleigh quotient iteration. SIAM J. Matrix Anal. Appl. 30 (2008), 346-363. DOI 10.1137/060671401 | MR 2399584 | Zbl 1165.65016
[29] Sorrentino, F., Tolić, D., Fierro, R., Picozzi, S., Gordon, J. R., Mammoli, A.: Stability analysis of a model for the market dynamics of a smart grid. 52nd IEEE Conference on Decision and Control IEEE, Los Alamitos (2013), 4964-4970. DOI 10.1109/CDC.2013.6760668
[30] Tolić, D.: $\mathcal{L}_p$-stability with respect to sets applied towards self-triggered communication for single-integrator consensus. 52nd IEEE Conference on Decision and Control IEEE, Los Alamitos (2013), 3409-3414. DOI 10.1109/CDC.2013.6760405
[31] Tolić, D., Jeličić, V., Bilas, V.: Resource management in cooperative multi-agent networks through self-triggering. IET Control Theory Appl. 9 (2015), 915-928. DOI 10.1049/iet-cta.2014.0576 | MR 3364336
[32] Tolić, D., Palunko, I., Ivanović, A., Car, M., Bogdan, S.: Multi-agent control in degraded communication environments. 2015 European Control Conference (ECC) IEEE, Los Alamitos (2015), 404-409. DOI 10.1109/ECC.2015.7330577 | MR 3364036
[33] Tomljanović, Z., Voigt, M.: Semi-active $\mathcal{H}_\infty$ damping optimization by adaptive interpolation. Numer. Linear Algebra Appl. 27 (2020), Article ID e2300, 17 pages. DOI 10.1002/nla.2300 | MR 4157212 | Zbl 1463.93076
[34] Wang, Y., Garcia, E., Casbeer, D., (eds.), F. Zhang: Cooperative Control of Multi-Agent Systems: Theory and Applications. John Wiley & Sons, Hoboken (2017). DOI 10.1002/9781119266235 | MR 3618878 | Zbl 1406.93005
[35] Yue, Y., Meerbergen, K.: Accelerating optimization of parametric linear systems by model order reduction. SIAM J. Optim. 23 (2013), 1344-1370. DOI 10.1137/120869171 | MR 3071415 | Zbl 1273.35279
[36] Zhou, K., Doyle, J. C., Glover, K.: Robust and Optimal Control. Prentice Hall, Upper Saddle River (1996). Zbl 0999.49500
Search
Partner of
