Decentralized Adaptive Control


In this chapter, the problem of designing decentralized adaptive state feedback controllers with corresponding adaptive law is presented a class of nonlinear time-varying and time-delay interconnected systems. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to decentralized strict feedback form are developed. In addition, a digital redesign of the analogue model-reference-based decentralized adaptive tracker is constructed for the sampled-data large scale system consisting of N interconnected linear subsystems, so that the system output will follow any trajectory specified at sampling instants.


Adaptive Controller Interconnected System Virtual Control Digital Controller Model Reference Adaptive Control 


  1. 1.
    Chang, Y. P., J. S. H. Tsai and L. S. Shieh, “Optimal Digital Redesign of Hybrid Cascaded Input-Delay Systems Under State and Control Constraints”, IEEE Trans. Circuits Syst., vol. 49, 2002, pp. 1382–1392. CrossRefGoogle Scholar
  2. 2.
    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. 1119–1124. MATHCrossRefGoogle Scholar
  3. 3.
    Datta, A., “Performance Improvement in Decentralized Adaptive Control: A Modified Model Reference Scheme”, IEEE Trans. Autom. Control, vol. 38, 1993, pp. 1717—1722. MATHCrossRefGoogle Scholar
  4. 4.
    Datta, A. and P. A. Ioannou, “Decentralized Indirect Adaptive Control of Interconnected Systems”, Int. J. Adapt. Control Signal Process., vol. 5, 1991, pp. 259–281. MATHCrossRefGoogle Scholar
  5. 5.
    Davison, E. J., “The Robust Decentralized Control of Servomechanism Problem for Composite System with Input-Output Interconnection”, IEEE Trans. Autom. Control, vol. 24, 1979, pp. 325–327. MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Gavel, D. T. and T. C. Hsia, “Decentralized Adaptive Control of Robotic Manipulators”, Proc. IEEE Int. Conf. Robotics Automat., 1987, pp. 1230—1235. Google Scholar
  7. 7.
    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
  8. 8.
    Goodwin, G. C. and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, New York, 1984. MATHGoogle Scholar
  9. 9.
    Guo, S. M., L. S. Shieh G. Chen and C. F. Lin, “Effective Chaotic Orbit Tracker: A Prediction-Based Digital Redesign Approach”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, 2000, pp. 1557–1570. MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Hammamed, A. and L. Radouane, “Decentralized Nonlinear Adaptive Feedback Stabilization of Large-Scale Interconnected Systems”, IEE Proc. D, vol. 130, 1983, pp. 57–62. Google Scholar
  11. 11.
    Hunt, L. R., R. Su and G. Meyer, “Global Transformations of Nonlinear Systems”, IEEE Trans. Autom. Control, vol. AC-28, no. 1, 1983, pp. 24–31. MathSciNetCrossRefGoogle Scholar
  12. 12.
    Huseyin, O., M. E. Sezer and D. D. Siljak, “Robust Decentralized Control Using Output Feedback”, IEE Proc. D, vol. 129, 1982, pp. 310–314. Google Scholar
  13. 13.
    Ikeda, K. and S. Shin, “Fault Tolerant Decentralized Control Systems Using Backstepping”, Proc. the 33rd Conference on Decision and Control, New Orleans, LA, 1995, pp. 2340—2345. Google Scholar
  14. 14.
    Ioannou, P. A. and P. V. Kokotovic, “Robust Redesign of Adaptive Control”, IEEE Trans. Autom. Control, vol. AC-29, 1984, pp. 202–211. CrossRefGoogle Scholar
  15. 15.
    Ioannou, P. A. and P. V. Kokotovic, “Decentralized Adaptive Control of Interconnected Systems with Reduced-Order Models”, Automatica, vol. 21, no. 2, pp. 401–412, 1985. MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Ioannou, P. A., “Decentralized Adaptive Control of Interconnected Systems”, IEEE Trans. Autom. Control, vol. AC-31, 1986, pp. 291–298. MathSciNetCrossRefGoogle Scholar
  17. 17.
    Ioannou, P. A. and J. Sun, Robust Adaptive Control, Prentice-Hall, New York, 1996. MATHGoogle Scholar
  18. 18.
    Isidori, A., Nonlinear Control Systems (2nd ed.), Springer, New York, 1989. MATHCrossRefGoogle Scholar
  19. 19.
    Jain, S., Adaptive Control of Nonlinear and Large-Scale Systems with Applications to Flexible Manipulators and Power Systems, Ph.D. dissertation, Polytechnic University, Brooklyn, New York, June 1995. Google Scholar
  20. 20.
    Kanellakopoulos, I., P. V. Kokotovic and A. S. Morse, “Systematic design of Adaptive Controllers for Feedback Linearizable Systems”, IEEE Trans. Autom. Control, vol. 36, no. 11, 1991, pp. 1241–1253. MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Krstic, M., I. Kanellakopoulos and P. V. Kokotovic, “Adaptive Nonlinear Control Without Overparameterization”, Syst. Control Lett., vol. 19, 1992, pp. 177–185. MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Mahmoud, M. S., M. F. Hassan and M. G. Darwish, Large Scale Control Systems: Theories and Techniques, Dekker, New York, 1985. MATHGoogle Scholar
  23. 23.
    Mahmoud, M. S. and S. Bingulac, “Robust Design of Stabilizing Controllers for Interconnected Time-Delay Systems”, Automatica, vol. 34, 1998, pp. 795–800. MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Mahmoud, M. S. and M. Zribi, “Robust and H oo Stabilization of Interconnected Systems with Delays”, IEE Proc., Control Theory Appl., vol. 145, 1998, pp. 558–567. CrossRefGoogle Scholar
  25. 25.
    Mahmoud, M. S., “On a Modeling Approach of Dynamical Systems: A Guided Tour”, Mediterr. J. Meas. Control, vol. 1, no. 1, 2005, pp. 8–17. Google Scholar
  26. 26.
    Mahmoud, M. S. and H. N. Nounou, “Dissipative Analysis and Synthesis of Time-Delay Systems”, Mediterr. J. Meas. Control, vol. 1, 2005, pp. 97–108. Google Scholar
  27. 27.
    Mirkin, B. M., “Decentralized Adaptive Control with Model Coordination for Large-Scale Time-Delay Systems”, Proc. 3rd European Control Conference, vol. 4, Roma, Italy, 1995, pp. 2946–2949. Google Scholar
  28. 28.
    Mirkin, B. M., “Decentralized Adaptive Controller with Zero Residual Tracking Errors”, Proc. 7th Mediterranean Conference on Control and Automation (MED99), Haifa, Israel, 1999, pp. 28–30. Google Scholar
  29. 29.
    Narendra, K. S. and N. O. Oleng, “Exact Output Tracking in Decentralized Adaptive Control Systems”, Center for Systems Science, Yale University, New Haven, CT, Tech. Rep. 0104, 2001. Google Scholar
  30. 30.
    Narendra, K. S. and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, New York, 1989. MATHGoogle Scholar
  31. 31.
    Narendra, K. S. and N. O. Oleng, “Exact Output Tracking in Decentralized Adaptive Control Systems”, IEEE Trans. Autom. Control, vol. AC-47, 2002, pp. 390–394. MathSciNetCrossRefGoogle Scholar
  32. 32.
    Ortega, R. and A. Herrera, “A Solution to the Decentralized Adaptive Stabilization Problem”, Syst. Control Lett., vol. 20, 1993, pp. 299–306. MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Oucheriah, S., “Decentralized Stabilization of Large-Scale Systems with Multiple Delays in the Interconnection”, Int. J. Control, vol. 73, 2000, pp. 1213–1223. MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Pagilla, P. R., “Robust Decentralized Control of Large-Scale Interconnected Systems: General Interconnections”, Proc. American Control Conference, San Diego, CA, 1999, pp. 4527–4531. Google Scholar
  35. 35.
    Popov, V. M., Hyperstability of Control Systems, Springer, New York, 1973. MATHCrossRefGoogle Scholar
  36. 36.
    Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, New York, 1976. MATHGoogle Scholar
  37. 37.
    Seto, D., A. M. Annaswamy and J. Baillieul, “Adaptive Control of Nonlinear Systems with a Triangular Structure”, IEEE Trans. Autom. Control, vol. 39, 1994, pp. 1411–1428. MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    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
  39. 39.
    Shi, L. and S. K. Singh, “Decentralized Control for Interconnected Uncertain Systems: Extensions to Higher Order Uncertainties”, Int. J. Control, vol. 57, no. 6, 1993, pp. 1453–1468. MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Wen, C., “Direct Decentralized Adaptive Control of Interconnected Systems Having Arbitrary Subsystem Relative Degrees”, Proc. 33rd Conference on Decision and Control, Lake Buena Vista, FL, 1994, pp. 1187–1192. Google Scholar
  41. 41.
    Wen, C., “Indirect Robust Totally Decentralized Adaptive Control of Continuous-Time Interconnected Systems”, IEEE Trans. Autom. Control, vol. 38, 1995, 1122–1126. Google Scholar
  42. 42.
    Wen, C. and Y. C. Soh, “Decentralized Adaptive Control Using Integrator Backstepping”, Automatica, vol. 33, 1997, pp. 1719–1724. MathSciNetCrossRefGoogle Scholar
  43. 43.
    Wu, H. S., “Decentralized Robust Control for a Class of Large-Scale Interconnected Systems with Uncertainties”, Int. J. Syst. Sci., vol. 20, 1989, pp. 2597–2608. MATHCrossRefGoogle Scholar
  44. 44.
    Zhang, Y., C. Wen and Y. C. Soh, “Robust Decentralized Adaptive Stabilization of Interconnected Systems with Guaranteed Transient Performance”, Automatica, vol. 36, 2000, pp. 907–915. MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Zhou, J. and C. Wen, “Decentralized Backstepping Adaptive Output Tracking of Interconnected Nonlinear Systems”, IEEE Trans. Autom. Control, vol. AC-53, 2008, pp. 2378–2384. MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

Personalised recommendations