Information Structure Constraints

Part of the Communications and Control Engineering book series (CCE)


Large-scale systems require control laws whose computation is efficient, and whose implementation entails a minimal amount of information exchange between the subsystems. In order to design such laws, it is necessary to develop versatile algorithms that can incorporate a broad range of information structure constraints. This problem has received considerable attention in recent years, particularly in the context of Linear Matrix Inequalities (LMIs) (see e.g., Boyd et al., 1994; Geromel et al., 1994; El Ghaoui and Niculescu, 2000; de Oliveira et al., 2000; Ayers and Paganini, 2002; Langbort et al., 2004; Šiljak and Zečević, 2005; Zečević and Šiljak, 2008, and the references therein). In this chapter we will adopt a similar approach, and utilize LMI optimization to obtain structurally constrained control laws that are suitable for complex systems. In doing so, we will rely on the mathematical framework proposed in Šiljak and Stipanović (2000) which will be extended in a number of different ways. We will also take into account the decomposition techniques described in Chap. 1, which suggest that the gain matrix structures shown in Figs. 2.1–2.3 are particularly desirable for large-scale applications.

In the sections that follow, we will describe how each of these structures can be obtained in an efficient manner, and examine a variety of possible applications.


Linear Matrix Inequality Gain Matrix Power System Stability Decentralize Control Overlap Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, B. D. O. and D. J. Clements (1981). Algebraic characterization of fixed modes in decentralized control. Automatica, 17, 703–712.CrossRefMathSciNetGoogle Scholar
  2. Ayres, G. and F. Paganini (2002). Convex synthesis of localized controllers for spatially invariant systems. Automatica, 38, 445–456.MATHCrossRefGoogle Scholar
  3. Bakule, L. (2008). Decentralized control: An overview. Annual Reviews in Control, 32, 87–98.CrossRefGoogle Scholar
  4. Bakule, L. and J. Rodellar (1995). Decentralized control and overlapping decompositions of mechanical systems. International Journal of Control, 61, 559–587.MATHCrossRefMathSciNetGoogle Scholar
  5. Bakule, L., J. Rodellar and J. Rossel (2000). Generalized selection of complementary matrices in the inclusion principle. IEEE Transactions on Automatic Control, 45, 1237–1243.MATHCrossRefGoogle Scholar
  6. Belmehdi, A. and D. Boukhetala (2002). Method to eliminate structurally fixed modes in decentralized control systems. International Journal of Systems Science, 33, 1249–1256.MATHCrossRefMathSciNetGoogle Scholar
  7. Bertsekas, D. P. and J. N. Tsitsiklis (1989). Parallel and Distributed Computation. Prentice-Hall, Upper Saddle River, NJ.MATHGoogle Scholar
  8. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, PA.MATHGoogle Scholar
  9. Chu, D. and D. D. Šiljak (2005). A canonical form for the inclusion principle of dynamic systems. SIAM Journal of Control and Optimization, 44, 969–990.MATHCrossRefGoogle Scholar
  10. Chu, D., Y. Ohta and D. D. Šiljak (2009). Inclusion principle for descriptor systems. IEEE Transactions on Automatic Control, 54, 3–18.CrossRefGoogle Scholar
  11. Cogil, R. and S. Lall (2004). Control design for topology-independent interconnected systems. Proceedings of the American Control Conference, Boston, MA, 3717–3722.Google Scholar
  12. Davison, E. J. and Ü. Özgüner (1983). Characterizations of decentralized fixed modes for interconnected systems. Automatica, 19, 169–182.MATHCrossRefGoogle Scholar
  13. Ebihara, Y. and T. Hagiwara (2003). Structured controller synthesis using LMI and alternating projection method. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 5632–5637.Google Scholar
  14. El Ghaoui, L. and S. Niculescu (Eds.) (2000). Advances in Linear Matrix Inequalities Methods in Control. SIAM, Philadelphia, PA.Google Scholar
  15. Feddema, J. T., C. Lewis and D. A. Schoenwald (2002). Decentralized control of cooperative robotic vehicles: Theory and application. IEEE Transactions on Robotics and Automation, 18, 852–864.CrossRefGoogle Scholar
  16. Franco, E., L. Magni, T. Parisini, M. M. Polycarpou and D. M. Raimondo (2008). Cooperative constrained control of distributed agents with nonlinear dynamics and delayed information exchange: A stabilizing receding-horizon approach. IEEE Transactions on Automatic Control, 53, 324–338.CrossRefMathSciNetGoogle Scholar
  17. Geromel, J. C., J. Bernussou and P. Peres (1994). Decentralized control through parameter space optimization. Automatica, 30, 1565–1578.MATHCrossRefMathSciNetGoogle Scholar
  18. Geromel, J. C., J. Bernussou and M. C. de Oliveira (1999). H -norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control. IEEE Transactions on Automatic Control, 44, 1449–1454.MATHCrossRefGoogle Scholar
  19. Godbole, D. N. and J. Lygeros (1994). Longitudinal control of the lead car of the platoon. IEEE Transactions on Vehicle Technology, 43, 1125–1135.CrossRefGoogle Scholar
  20. Golub, G. and C. van Loan (1996). Matrix Computations. Johns Hopkins University Press, Baltimore, MD.MATHGoogle Scholar
  21. Iftar, A. (1993). Decentralized estimation and control with overlapping input, state and output decomposition. Automatica, 29, 511–516.MATHCrossRefMathSciNetGoogle Scholar
  22. Iftar, A. and Ü. Özgüner (1990). Contractible controller design and optimal control with state and input inclusion. Automatica, 26, 593–597.MATHCrossRefGoogle Scholar
  23. Iftar, A. and U. Özgüner (1998). Overlapping decompositions, expansions, contractions and stability of hybrid systems. IEEE Transactions on Automatic Control, 43, 1040–1055.MATHCrossRefGoogle Scholar
  24. Ikeda, M. (1989). Decentralized control of large-scale systems. In: Three Decades of Mathematical System Theory, H. Nijmeijer and J. M. Schumacher (Eds.), Springer, Berlin, 135, 219–242.Google Scholar
  25. Ikeda, M. and D. D. Šiljak (1986). Overlapping decentralized control with input, state and output inclusion. Control Theory and Advanced Technology, 2, 155–172.Google Scholar
  26. Ikeda, M., D. D. Šiljak and D. E. White (1984). An inclusion principle for dynamic systems. IEEE Transactions on Automatic Control, 29, 244–249.MATHCrossRefGoogle Scholar
  27. Ilić, M. and J. Zaborszky (2000). Dynamics and Control of Large Electric Power Systems. Wiley, New York.Google Scholar
  28. Jamshidi, M. (1997). Large-Scale Systems: Modelling, Control and Fuzzy Logic. Prentice-Hall, Upper Saddle River, NJ.Google Scholar
  29. Jiang, H., H. Cai, J. Dorsey and Z. Qu (1997). Toward a globally robust decentralized control for large-scale power systems. IEEE Transactions on Control System Technology, 5, 309–319.CrossRefGoogle Scholar
  30. Kitts, C. A., I. Mas (2009). Cluster space specification and control of mobile multirobot systems. IEEE/ASME Transactions on Mechatronics, 14, 207–218.CrossRefGoogle Scholar
  31. Kundur, P. (1994). Power System Stability and Control. McGraw-Hill, New York.Google Scholar
  32. Langbort, C., R. S. Chandra and R. d’Andrea (2004). Distributed control design for systems interconnected over an arbitrary graph. IEEE Transactions on Automatic Control, 49, 1502–1519.CrossRefMathSciNetGoogle Scholar
  33. Lavaei, J. and A. G. Aghdam (2008). Control of continuous-time LTI systems by means of structurally constrained controllers. Automatica, 44, 141–148.MATHCrossRefMathSciNetGoogle Scholar
  34. Lavaei, J. and A. G. Aghdam (2009). Overlapping control design for multi-channel systems. Automatica, 45, 1326–1331.MATHCrossRefMathSciNetGoogle Scholar
  35. Li, Q., Z.-P. Jiang (2008). Two decentralized heading consensus algorithms for nonlinear multi-agent systems. Asian Journal of Control, 10, 187–200.CrossRefMathSciNetGoogle Scholar
  36. Li, K., E. B. Kosmatopoulos, P. A. Ioannou and H. Ryaciotaki-Boussalis (2000). Large segmented telescopes: Centralized, decentralized and overlapping control designs. IEEE Control Systems Magazine, 20, 59–72.CrossRefGoogle Scholar
  37. Lin, Z., B. Francis and M. Maggiore (2007). State agreement for continuous-time coupled nonlinear systems. SIAM Journal of Control and Optimization, 46, 288–307.MATHCrossRefMathSciNetGoogle Scholar
  38. Lunze, J. (1992). Feedback Control of Large-Scale Systems. Prentice-Hall, Upper Saddle River, NJ.MATHGoogle Scholar
  39. Michel, A. N. and R. K. Miller (1977). Qualitative Analysis of Large Scale Dynamic Systems. Academic, New York.Google Scholar
  40. Nesterov, Y. and A. Nemirovskii (1994). Interior Point Polynomial Methods in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA.Google Scholar
  41. Okou, F. A., O. Akhrif and L.-A. Dessaint (2005). Decentralized multivariable voltage and speed regulator for large-scale power systems with guarantee of stability and transient performance. International Journal of Control, 78, 1343–1358.MATHCrossRefMathSciNetGoogle Scholar
  42. de Oliveira, M., J. C. Geromel and J. Bernussou (2000). Design of dynamic output feedback decentralized controllers via a separation procedure. International Journal of Control, 73, 371–381.MATHCrossRefMathSciNetGoogle Scholar
  43. Pai, M. A. (1989). Energy Function Analysis for Power System Stability. Kluwer, Boston, MA.Google Scholar
  44. Sauer, P. W. and M. A. Pai (1998). Power System Dynamics and Stability. Prentice-Hall, Upper Saddle River, NJ.Google Scholar
  45. Sezer, M. E. and D. D. Šiljak (1981). Structurally fixed modes. Systems and Control Letters, 1, 60–64.MATHCrossRefMathSciNetGoogle Scholar
  46. Sezer, M. E. and D. D. Šiljak (1996). Decentralized Control. In: The Control Handbook, W. Levine (Ed.), CRC Press, Boca Raton, FL, 779–793.Google Scholar
  47. Shladover, S. E. (1991). Longitudinal control of automotive vehicles in close formation platoons. Journal of Dynamic Systems, Measurement and Control, 113, 231–241.CrossRefGoogle Scholar
  48. Šiljak, D. D. (1978). Large-Scale Dynamic Systems: Stability and Structure. North Holland, New York.MATHGoogle Scholar
  49. Šiljak, D. D. (1991). Decentralized Control of Complex Systems. Academic, Cambridge, MA.Google Scholar
  50. Šiljak, D. D. (1996). Decentralized control and computation: Status and Prospects. Annual Reviews in Control, 20, 131–141.CrossRefGoogle Scholar
  51. Šiljak, D. D. and A. I. Zečević (1999). Large-Scale and Decentralized Systems. In: Wiley Encyclopaedia of Electrical and Electronics Engineering, J. G. Webster (Ed.), Wiley, New York, 209–224.Google Scholar
  52. Šiljak, D. D. and D. M. Stipanović (2000). Robust stabilization of nonlinear systems: The LMI approach. Mathematical Problems in Engineering, 6, 461–493.MATHCrossRefGoogle Scholar
  53. Šiljak, D. D. and A. I. Zečević (2005). Control of large-scale systems: Beyond decentralized feedback. Annual Reviews in Control, 29, 169–179.CrossRefGoogle Scholar
  54. Šiljak, D. D., D. M. Stipanović and A. I. Zečević (2002). Robust decentralized turbine/governor control using linear matrix inequalities. IEEE Transactions on Power Systems, 17, 715–722.CrossRefGoogle Scholar
  55. Sojoudi, S. and A. G. Aghdam (2009). Overlapping control systems with optimal information exchange. Automatica, 45, 1176–1181.MATHCrossRefMathSciNetGoogle Scholar
  56. Speyer, J. L., I. Seok and A. Michelin (2008). Decentralized control based on the value of information in large vehicle arrays. Proceedings of the American Control Conference, Seattle, WA, 5047–5054.Google Scholar
  57. Stanković, S. S. and D. D. Šiljak (2001). Contractibility of overlapping decentralized control. Systems and Control Letters, 44, 189–199.MATHCrossRefMathSciNetGoogle Scholar
  58. Stanković, S. S. and D. D. Šiljak (2003). Inclusion principle for linear time-varying systems. SIAM Journal on Control and Optimization, 42, 321–341.MATHCrossRefMathSciNetGoogle Scholar
  59. Stanković, S. S. and D. D. Šiljak (2008). Stabilization of fixed modes in expansion of LTI systems. Systems and Control Letters, 57, 365–370.MATHCrossRefMathSciNetGoogle Scholar
  60. Stanković, S. S., X. B. Chen, M. R. Mataušek and D. D. Šiljak (1999). Stochastic inclusion principle applied to decentralized automatic generation control. International Journal of Control, 72, 276–288.MATHCrossRefMathSciNetGoogle Scholar
  61. Stanković, S. S., M. J. Stanojević and D. D. Šiljak (2000). Decentralized overlapping control of a platoon of vehicles. IEEE Transactions on Control System Technology, 8, 816–832.CrossRefGoogle Scholar
  62. Stanković, S. S., M. S. Stanković and D. M. Stipanović (2009). Consensus based overlapping decentralized estimator. IEEE Transactions on Automatic Control, 54, 410–415.CrossRefGoogle Scholar
  63. Stipanović, D. M., G. Inalhan, R. Teo and C. Tomlin (2004). Decentralized overlapping control of a formation of unmanned aerial vehicles. Automatica, 40, 1285–1296.MATHCrossRefGoogle Scholar
  64. Stipanović, D. M., P. F. Hokayem, M. W. Spong and D. D. Šiljak (2007). Cooperative avoidance control for multiagent systems. Journal of Dynamic Systems, Measurement, and Control, 129, 699–707.CrossRefGoogle Scholar
  65. Swarnakar, A., H. J. Marquez and T. Chen (2008). A design framework for overlapping controllers and its industrial application. Control Engineering Practice, 17, 97–111.CrossRefGoogle Scholar
  66. Swaroop, D., J. K. Hedrick, C. C. Chien and P. A. Ioannou (1994). Comparison of spacing and headway control laws for automatically controlled vehicles. Vehicle System Dynamics, 23, 597–625.CrossRefGoogle Scholar
  67. Tamura, H. and T. Yoshikawa (1990). Large-Scale Systems Control and Decision Making. Marcel Dekker, New York.MATHGoogle Scholar
  68. Tanino, T. and M. Tanaka (1993). Elimination of fixed modes in linear control structures. Proceedings of the 12th IFAC World Congress, Sydney, Australia, 163–166.Google Scholar
  69. Voulgaris, P. G. (2003). Optimal control design under structural and communication constraints. In: Multidisciplinary Research in Control, L. Giarré and B. Bamieh (Eds.), Springer, Berlin, 47–61.CrossRefGoogle Scholar
  70. Wang, S. H. and E. J. Davison (1973). On the stabilization of decentralized control systems. IEEE Transactions on Automatic Control, 18, 473–478.MATHCrossRefMathSciNetGoogle Scholar
  71. Wright, S. (1997). Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA.MATHGoogle Scholar
  72. Wu, H. (2003). Decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections. International Journal of Control, 76, 253–265.MATHCrossRefMathSciNetGoogle Scholar
  73. Yakubovich, V. A. (1977). The S-procedure in nonlinear control theory. Vestnik Leningrad University. Mathematics, 4, 73–93.Google Scholar
  74. Zečević, A. I. and D. D. Šiljak (2004). A preconditioning strategy for overlapping control design using linear matrix inequalities. Technical ReportECS-0099469/35, Santa Clara University, Santa Clara, CA.Google Scholar
  75. Zečević, A. I. and D. D. Šiljak (2005a). Global low-rank enhancement of decentralized control for large-scale systems. IEEE Transactions on Automatic Control, 50, 740–744.CrossRefGoogle Scholar
  76. Zečević, A. I. and D. D. Šiljak (2005b). A new approach to control design with overlapping information structure constraints. Automatica, 41, 265–272.MATHCrossRefGoogle Scholar
  77. Zečević, A. I. and D. D. Šiljak (2005c). Robust control of large power systems via convex optimization. In: Applied Mathematics for Restructured Electric Power Systems, J. H. Chow, F. Wu and J. Momoh (Eds.), Springer, New York, 139–158.Google Scholar
  78. Zečević, A. I. and D. D. Šiljak (2008). Control design with arbitrary information structure constraints. Automatica, 44, 2642–2647.MATHCrossRefGoogle Scholar
  79. Zhai, G., M. Ikeda and Y. Fujisaki (2001). Decentralized H controller design: A matrix inequality approach using a homotopy method. Automatica, 37, 565–572.MATHCrossRefMathSciNetGoogle Scholar
  80. Zheng, Y. and R. J. Evans (2005). Information structure considerations for decentralized large-scale systems. Asian Journal of Control, 7, 424–432.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Aleksandar I. Zečević
    • 1
  • Dragoslav D. Šiljak
    • 1
  1. 1.Dept. Electrical EngineeringSanta Clara UniversitySanta ClaraUSA

Personalised recommendations