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Decentralized Control of Nonlinear Systems II

  • Magdi S. Mahmoud

Abstract

In this chapter, we start our examination of the development of decentralized control techniques for interconnected systems where we focus on the classes of nonlinear continuous-time systems. We focus on interconnected minimum-phase nonlinear systems with parameter uncertainty and bounded and/or strong nonlinear interconnections. The objective is to design a robust decentralized controller such that the closed-loop large-scale interconnected nonlinear system is globally asymptotically stable for all admissible uncertain parameters and interconnections. The design is recursive in nature. By employing \({\mathcal{H}}_{\infty}\) performance, the solution of the decentralized control problem is attained via the Hamilton-Jacobi-Isaacs (HJI) inequalities. Finally, a decentralized output-feedback tracking problem with disturbance attenuation is addressed for a new class of large-scale and minimum-phase nonlinear systems. Application of decentralized stabilization and excitation controls of multimachine power systems are demonstrated.

Keywords

Interconnected System Guarantee Cost Control Power Angle Multimachine Power System Interconnected Nonlinear System 
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.

References

  1. 1.
    Al-Fuhaid, A. S., M. S. Mahmoud and F. A. Saleh, “Stabilization of Power Systems by Decentralized Systems and Control Theory”, Electr. Mach. Power Syst., vol. 21, no. 3, 1993, pp. 293–318. CrossRefGoogle Scholar
  2. 2.
    Ball, J. A., J. W. Helton and M. L. Walker, “\({\mathcal{H}}_{\infty}\) Control for Nonlinear System with Output Feedback”, IEEE Trans. Autom. Control, vol. 38, 1993, pp. 549–559. MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bergen, A. R., Power Systems Analysis, Prentice-Hall, Englewood Cliffs, 1986. Google Scholar
  4. 4.
    Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994. MATHCrossRefGoogle Scholar
  5. 5.
    Chapman, J. W., M. D. Ilic, C. A. King, L. Eng and H. Kaufman, “Stabilizing a Multimachine Power System via Decentralized Feedback Linearizing Excitation Control”, IEEE Trans. Power Syst., vol. 8, no. 3, 1993, pp. 830–839. CrossRefGoogle Scholar
  6. 6.
    Chen, Y. H., G. Leitmann and Z. K. Xiong, “Robust Control Design for Interconnected Systems with Time-Varying Uncertainties”, Int. J. Control, vol. 54, 1991, pp. 1457–1477. Google Scholar
  7. 7.
    Freeman, R. A., P. V. Kokotovic, “Design of ‘Softer’ Robust Nonlinear Control Law”, Automatica, vol. 29, 1993, pp. 1425–1473. MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gahinet, P. and P. Apkarian, “A Linear Matrix Inequality Approach to \({\mathcal{H}}_{\infty}\) Control”, Int. J. Robust Nonlinear Control, vol. 4, 1994, pp. 421–448. MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Gahinet, P., A. Nemirovski, A.J. Laub and M. Chilali, LMI Control Toolbox, The Math Works, Natick, 1995. Google Scholar
  10. 10.
    Gao, L., L. Chen, Y. Fan and H. Ma, “Nonlinear Control Design for Power Systems”, Automatica, vol. 28, 1992, pp. 975–979. MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Gavel, D. T. and D. D. Siljak, “Decentralized Adaptive Control: Structural Conditions for Stability”, IEEE Trans. Autom. Control, vol. 34, no. 4, 1989, pp. 413–426. MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Gong, Z., C. Wen and D. P. Mital, “Decentralized Robust Controller Design for a Class of Interconnected Uncertain Systems with Unknown Bound of Uncertainty”, IEEE Trans. Autom. Control, vol. 41, no. 6, 1996, pp. 850–854. MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Guo, Y., Jiang, Z. P., and D. J. Hill, “Decentralized Robust Disturbance Attenuation for a Class of Large-Scale Nonlinear Systems”, Syst. Control Lett., vol. 17, 1999, pp. 71–85. MathSciNetCrossRefGoogle Scholar
  14. 14.
    Guo, Y., D. J. Hill and Y. Wang, “Nonlinear Decentralized Control of Large-Scale Power Systems”, Automatica, vol. 36, 2000, pp. 1275–1289. MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Han, M. C. and Y. H. Chen, “Decentralized Control Design: Uncertain Systems with Strong Interconnections”, Int. J. Control, vol. 61, no. 6, 1995, pp. 1363–1385. MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Ikeda, M., and D. D. Siljak, “Optimality and Robustness of Linear Quadratic Control for Nonlinear Systems”, Automatica, vol. 26, 1990, pp. 499–511. MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Isidori, A., Nonlinear Control Systems (3rd ed.), Springer, New York, 1995. MATHCrossRefGoogle Scholar
  18. 18.
    Isidori, A., “Global Almost Disturbance Decoupling with Stability for Non Minimum-Phase Single-Input Single-Output Nonlinear Systems”, Syst. Control Lett., vol. 28, 1996, pp. 115–122. MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Isidori, A., and W. Kang, “\({\mathcal{H}}_{\infty}\) Control via Measurement Feedback for General Nonlinear Systems”, IEEE Trans. Autom. Control, vol. 40, 1995, pp. 466–472. MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Isidori, A., and W. Lin, “Global \({\mathcal{L}}_{2}\)-Gain State Feedback Design for a Class of Nonlinear Systems”, Syst. Control Lett., vol. 34, 1998, pp. 295–302. MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Jain, S. and F. Khorrami, “Decentralized Adaptive Control of a Class of Large-Scale Interconnected Systems”, IEEE Trans. Autom. Control, vol. 42, no. 2, 1997, pp. 136–154. MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Jiang, Z. P., “Decentralized and Adaptive Nonlinear Tracking of Large-Scale Systems via Output Feedback”, IEEE Trans. Autom. Control, vol. 45, no. 11, 2000, pp. 2122–2128. MATHCrossRefGoogle Scholar
  23. 23.
    Jiang, Z. P., “Global Output Feedback Control with Disturbance Attenuation for Minimum-Phase Nonlinear Systems”, Syst. Control Lett., vol. 39, no. 3, 2000, pp. 155–164. MATHCrossRefGoogle Scholar
  24. 24.
    Khalil, H. K., Nonlinear Systems (2nd ed.), Prentice-Hall, Upper Saddle-River, 1996. Google Scholar
  25. 25.
    Khargonekar, P. P., I. R. Petersen, and K. Zhou, “Robust Stabilization of Uncertain Systems: Quadratic Stabilizability and \({\mathcal{H}}_{\infty}\) Control Theory”, IEEE Trans. Autom. Control, vol. 35, 1990, pp. 356–361. MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    King, C. A., Chapman, W. J., and M. D. Ilic, “Feedback Linearizing Excitation Control on Full-Scale Power System Model”, IEEE Trans. Power Syst., vol. 9, 1994, pp. 1102–1109. CrossRefGoogle Scholar
  27. 27.
    Krstić, M., I. Kanellakopoulos, P. V. Kokotović, Nonlinear and Adaptive Control Design, Wiley, New York, 1995. Google Scholar
  28. 28.
    Kundur, P., Power System Stability and Control, McGraw-Hill, New York, 1994. Google Scholar
  29. 29.
    Lin, W., “Global Robust Stabilization of Minimum-Phase Nonlinear Systems with Uncertainty”, Automatica, vol. 33, no. 3, 1997, pp. 521–526. CrossRefGoogle Scholar
  30. 30.
    Lin, W., and L. Xie, “A Link Between \({\mathcal{H}}_{\infty}\) Control of a Discrete-Time Nonlinear System and Its Linearization”, Int. J. Control, vol. 69, 1998, pp. 301–314. MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Lu, Q., Y. Sun, Z. Xu and T. Mochizuki, “Decentralized Nonlinear Optimal Excitation Control”, IEEE Trans. Power Syst., vol. 11, 1996, pp. 1957–1962. CrossRefGoogle Scholar
  32. 32.
    Marino, R. and P. Tomei, “Robust Stabilization of Feedback Linearizable Time-Varying Uncertain Nonlinear Systems”, Automatica, vol. 29, 1993, pp. 181–189. MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Marino, R., and W. Respondek, A. J. van der Schaft and P. Tomei, “Nonlinear \({\mathcal{H}}_{\infty}\) Almost Disturbance Decoupling”, Syst. Control Lett., vol. 23, 1994, pp. 159–168. MATHCrossRefGoogle Scholar
  34. 34.
    Marino, R. and P. Tomei, Nonlinear Control Design: Geometric, Adaptive and Robust, Prentice-Hall, Englewood Cliffs, 1995. MATHGoogle Scholar
  35. 35.
    Marino, R., and P. Tomei, “Nonlinear Output Feedback Tracking with Disturbance Attenuation”, IEEE Trans. Autom. Control, vol. 44, 1999, pp. 18–28. MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Mazenc, F., L. Praly and W. P. Dayawansa, “Global Stabilization by Output Feedback: Examples and Counter Examples”, Syst. Control Lett., vol. 23, 1994, pp. 17–32. MathSciNetCrossRefGoogle Scholar
  37. 37.
    Paz, R. A., “Decentralized Control”, Proc. American Control Conference, San Francisco, California, 1993, pp. 2381–2385. Google Scholar
  38. 38.
    Petersen, I. R., and D. C. McFarlane, “Optimal Guaranteed Cost Control and Filtering for Uncertain Systems”, IEEE Trans. Autom. Control, vol. 39, 1994, pp. 1971–1977. MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    Petersen, I. R., D. C. McFarlane, and M. A. Rotea, “Optimal Guaranteed Cost Control of Discrete-Time Uncertain Linear Systems”, Int. J. Robust Nonlinear Control, vol. 8, 1998, pp. 649–657. MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Praly, L., and Z. P. Jiang, “Stabilization by Output Feedback for Systems with ISS Inverse Dynamics”, Syst. Control Lett., vol. 21, 1993, pp. 19–33. MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Qiu, Z., J. F. Dorsey, J. Bond, and J. D. McCalley, “Application of Robust Control to Sustained Oscillations in Power Systems”, IEEE Trans. Circuits Syst. I, vol. 39, 1992, pp. 470–476. CrossRefGoogle Scholar
  42. 42.
    Qu, Z., “Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions”, Automatica, vol. 29, 1993, pp. 985–998. MATHCrossRefGoogle Scholar
  43. 43.
    Saberi, A., and H. K. Khalil, “Decentralized Stabilization of Interconnected Systems Using Output Feedback”, Int. J. Control, vol. 41, 1995, pp. 1461–1475. MathSciNetCrossRefGoogle Scholar
  44. 44.
    Shi, L. and S. K. Singh, “Decentralized Adaptive Controller Design for Large-Scale Systems with Higher-Order Uncertainties”, IEEE Trans. Autom. Control, vol. 37, no. 8, 1992, pp. 1106–1118. MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Shi, L. and S. K. Singh, “Decentralized Controller Design for Interconnected Uncertain Systems: Extensions to Higher-Order Uncertainties”, Int. J. Control, vol. 57, no. 6, 1993, pp. 1453–1468. MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    Siljak, D. D., Decentralized Control of Complex Systems, Academic Press, New York, 1991. Google Scholar
  47. 47.
    Sontag, E. D., “Comments on Integral Variants of ISS”, Syst. Control Lett., vol. 34, 1998, pp. 93–100. MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Sontag, E. D., and Y. Wang, “On Characterizations of the Input-to-State Stability Property”, Syst. Control Lett., vol. 24, 2000, pp. 351–359. MathSciNetCrossRefGoogle Scholar
  49. 49.
    Su, W., L. Xie and C. E. De Souza, “Global Robust Disturbance Attenuation and Almost Disturbance Decoupling for Uncertain Cascaded Nonlinear Systems”, Automatica, vol. 35, 1999, pp. 697–707. MATHCrossRefGoogle Scholar
  50. 50.
    Tezcan, I. E., and Basar, “Disturbance Attenuating Adaptive Controllers for Parametric Strict Feedback Nonlinear Systems with Output Measurements”, J. Dyn. Syst. Meas. Control, vol. 121, 1999, pp. 48–57. CrossRefGoogle Scholar
  51. 51.
    Van der Schaft, A. J., \({\mathcal{L}}_{2}\) -Gain and Passivity Techniques in Nonlinear Control, Springer, London, 1996. Google Scholar
  52. 52.
    Van Der Schaft, A. J., “\({\mathcal{L}}_{2}\)-Gain Analysis of Nonlinear Systems and Nonlinear \({\mathcal{H}}_{\infty}\) Control IEEE Trans. Autom. Control, vol. 37, 1992, pp. 770–784. MATHCrossRefGoogle Scholar
  53. 53.
    Veillette, R. J., J. V. Medanic, and W. R. Perkins, “Design of Reliable Control Systems”, IEEE Trans. Autom. Control, vol. 37, 1992, pp. 290–304. MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    Wang, Y., G. Guo and D. J. Hill, “Robust Decentralized Nonlinear Controller Design for Multimachine Power Systems”, Automatica, vol. 33, 1997. Google Scholar
  55. 55.
    Wang, Y., C. E. De Souza and L. Xie, “Decentralized Output Feedback Control of Interconnected Uncertain Systems”, Proc. the 2nd European Control Conference, Groningen, The Netherlands, 1993, pp. 1826–1831. Google Scholar
  56. 56.
    Wang, Y., L. Xie, and C. E. de Souza, “Robust Control of a Class of Uncertain Nonlinear Systems”, Syst. Control Lett., vol. 19, 1992, pp. 139–149. CrossRefGoogle Scholar
  57. 57.
    Wang, Y., L. Xie, D. J. Hill and R. H. Middleton, “Robust Nonlinear Controller Design for Transient Stability Enhancement of Power Systems”, Proc. 31st IEEE Conf. Decision and Control, Tucson, AZ, 1992, pp. 1117–1122. Google Scholar
  58. 58.
    Wang, Y., C. E. de Souza, and L. Xie, “Decentralized Output Feedback Control of Interconnected Uncertain Systems”, Proc. Europ. Contr. Conf., Groningen, The Netherlands, 1993, pp. 1826–1831. Google Scholar
  59. 59.
    Wen, C., and Y. C. Soh, “Decentralized Adaptive Control Using Integrator Backstepping”, Automatica, vol. 33, 1997, pp. 1719–1724. MathSciNetCrossRefGoogle Scholar
  60. 60.
    Xie, S., L. Xie and W. Lin, “Global \({\mathcal{H}}_{\infty}\) Control for a Class of Interconnected Nonlinear Systems”, Technical Report, School of EEE, Nanyang Technological University, Singapore, 1998. Google Scholar
  61. 61.
    Xie, L., and Y. C. Soh, “Guaranteed Cost Control of Uncertain Discrete-Time Systems”, Control Theory Adv. Technol., vol. 10, 1995, pp. 1235–1251. MathSciNetGoogle Scholar
  62. 62.
    Yan, X. -G., J.-J. Wang, X.-Y. Lu and S.-Y. Zhang, “Decentralized Output Feedback Robust Stabilization for a Class of Nonlinear Interconnected Systems with Similarity”, IEEE Trans. Autom. Control, vol. 43, 1998, pp. 294–299. MathSciNetMATHCrossRefGoogle Scholar
  63. 63.
    Zribi, M., M. S. Mahmoud, M. Karkoub and T. Li, “\({\mathcal{H}}_{\infty}\)-Controllers for Linearized Time-Delay Power Systems”, IEE Proc., Gener. Transm. Distrib., vol. 147, no. 6, 2000, pp. 401–408. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Systems EngineeringKing Fahd Univ. of Petroleum & MineralsDhahranSaudi Arabia

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