International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Advances in Nonlinear Predictive Control: A Survey on Stability and Optimality

  • Kwon, Wook-Hyun (Control Information Systems Lab., School of Electrical Engineering and Computer Science, Seoul National University) ;
  • Han, Soo-Hee (Control Information Systems Lab., School of Electrical Engineering and Computer Science, Seoul National University) ;
  • Ahn, Choon-Ki (Control Information Systems Lab., School of Electrical Engineering and Computer Science, Seoul National University)
  • Published : 2004.03.01
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Abstract

Some recent advances in stability and optimality for the nonlinear receding horizon control (NRHC) or the nonlinear model predictive control (NMPC) are assessed. The NRHCs with terminal conditions are surveyed in terms of a terminal state equality constraint, a terminal cost, and a terminal constraint set. Other NRHCs without terminal conditions are surveyed in terms of a control Lyapunov function (CLF) and cost monotonicity. Additional approaches such as output feedback, fuzzy, and neural network are introduced. This paper excludes the results for linear receding horizon controls and concentrates only on the analytical results of NRHCs, not including applications of NRHCs. Stability and optimality are focused on rather than robustness.

Keywords

References

  1. Advances in Model-Based Predictive Control D. W. Clarke
  2. Asian Control Conference Advances in predictive control : theory and application W. H. Kwon
  3. Fiflh International Conference on Chemical Process Control Recent advances in model predictive control and other related areas J. H. Lee;B. Cooley
  4. Fiflh International Conference on Chemical Process Control Nonlinear model predictive control An assessment D. Q. Mayne
  5. Fiflh International Conference on Chemical Process Control An overview of industrial model predictive control technology S. J. Qun;T. A. Badgwell
  6. Computers and Chemical Engineering v.23 An overview of industrial model predictive control technology M. Moran;J. H. Lee https://doi.org/10.1016/S0098-1354(98)00301-9
  7. Automatica v.36 Constrained model predictive control Stability and optimality D. Q. Mayne;J. B. Rawlings;C. V. Rao;P. O. M. Scokaert https://doi.org/10.1016/S0005-1098(99)00214-9
  8. Journal of Process Control v.8 Advances in nonlinear programming concepts for process control L. T. Biegler https://doi.org/10.1016/S0959-1524(98)00009-2
  9. IEEE Proc.-Control Theory Application v.147 no.4 Model predictive control of nonlinear systems : Computational burden and stability W. H. Chen;D. J. Balance;J. O. Reilly https://doi.org/10.1049/ip-cta:20000379
  10. J. of Optimization Theory and Applications v.57 Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximation S. S. Keerthi;E. G. Gilbert https://doi.org/10.1007/BF00938540
  11. IEEE Trans. on Automatic Control v.35 no.7 Receding horizon control of nonlinear systems D. Mayne;H. Michalska https://doi.org/10.1109/9.57020
  12. Systems and Control Letters v.16 Receding horizon control of nonlinear systems without differentiability of optimal value function H. Michalska;D. Mayne https://doi.org/10.1016/0167-6911(91)90006-Z
  13. Int. J. Contr. v.62 no.5 Receding horizon control and discontinuous state feedback stabilization B. S. Meadows;M. A. Henson;J. W. Eaton;J. B. Rawlings https://doi.org/10.1080/00207179508921593
  14. IEEE Trans. Automat. Contr. v.41 no.3 On the robustness of receding-horizon control with tenninal constraints G. D. Nicolao;L. Magni;R. Scattolini https://doi.org/10.1109/9.486649
  15. IEEE Thans. Automat. Contr. v.43 no.7 Stabilizing receding-horizon control of nonlinear time-varying systems G. De Nicolao;L. Magni;R. Scattolini https://doi.org/10.1109/9.701133
  16. System Control Letters v.32 Stability margins of nonlinear receding horizon control via inverse optimality L. Magni;R. Sepulchre https://doi.org/10.1016/S0167-6911(97)00079-0
  17. IEEE Trans. Automat. Contr. v.38 no.11 Robust receding horizon control of constrained non-linear systems H. Michalska;D. Mayne https://doi.org/10.1109/9.262032
  18. European Journal of Control v.2 Dual receding horizon control of constrained discretetime systems L. Chisci;A. Lombardi;E. Mosca https://doi.org/10.1016/S0947-3580(96)70052-3
  19. IEEE Trans. Automat. Contr. v.44 no.3 Suboptimal model predictive control (feasibility implies stability) P. Scokaert;D. Mayne;J. Rawlings https://doi.org/10.1109/9.751369
  20. American Control Conference Estimating quadratic stability domains by nonsmooth optimization J. Hauser;M. Lai
  21. IEEE Trans. on Automatic Control v.47 no.4 Toward infinite-horizon optimality in nonlinear model predictive control B. Hu;A. Linnemann https://doi.org/10.1109/9.995049
  22. Automatica v.34 A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability H. Chen;F. Allgower https://doi.org/10.1016/S0005-1098(98)00073-9
  23. Automatica v.31 no.10 A receding-horizon regulator for nonlinear systems and a neural approximation T. Parisini;R. Zoppoli https://doi.org/10.1016/0005-1098(95)00044-W
  24. IEEE Trans. on Automatic control v.46 no.5 Unconstrained receding-horizon control of nonlinear systems A. Jadbabaie;J. Yu;J. Hauser https://doi.org/10.1109/9.920800
  25. Automatica v.37 no.9 A stabilizing model-based predictive control for nonlinear systems L. Magni;G. De Nicolao;L. Magnani;R. Scattolini https://doi.org/10.1016/S0005-1098(01)00083-8
  26. Automatica v.31 no.9 Stability of a truncated infinite constrained receding horizon control scheme : The general discrete nonlinear case M. Alamir;G. Bomard https://doi.org/10.1016/0005-1098(95)00042-U
  27. Proc. of 38 th IEEE conference on decision and control On stabilizing receding horizon control for nonlinear discrete time systems G. De Nicolao;L. Magnani;L. Magni;R. Scattolini
  28. Proc. of the IMACS multiconference CESA v.1 Stabilizing nonlinear receding horizon control via a nonquadratic penalty G. De Nicolao;L. Magni;R. Scattolini
  29. International Symposium on Nonlinear Model Predictive Control : Assessment and Future Directions Stability and robustness of nonlinear receding horizon control G. De Nicolao;L. Magni;R. Scattolini
  30. IEEE Trans. on Automatic Control v.48 no.10 Mm-max model predictive control of nonlinear systems using discontinuous feedbacks F. A. C. C. Fontes;L. Magni https://doi.org/10.1109/TAC.2003.817915
  31. Journal of Process Control v.12 A scheduling quasi min max model predictive control algorithm for nonlinear systems Y. Lu;Y Arkun https://doi.org/10.1016/S0959-1524(01)00055-5
  32. International Workshop on Nonlinear Predictive Control Min-max receding horizon control of constrained, piecewise affine systems B. Kerrigan;D. Mayne;J. Maciejowski;J. Lygeros
  33. IEE Proc., Control Theory Application v.147 Receding horizon $H_{\infty}$ Predictive control for systems with input saturations Y. I. Lee https://doi.org/10.1049/ip-cta:20000258
  34. Automatica v.37 A receding horizon approach to the nonlinear $H_{\infty}$ control problem L. Magni;H. Nijmeijer;A. J. van der Schaft https://doi.org/10.1016/S0005-1098(00)00166-7
  35. Americal Control Conference A game theoretic approach to nonlinear robust receding horizon control of constrained systems H. Chen;C. W. Scherer;F. Aligower
  36. IEE Proc. Control Theory Application Receding horizon $H_{\infty}$ control for nonlinear discrete-time systems E. Gyurkovics
  37. IEEE Trans. Automat. Contr. v.45 no.5 A receding horizon generalization of pointwise min-norm controllers J. Primbs;V. Nevistic;J. Doyle https://doi.org/10.1109/9.855550
  38. American Control Conference Stabilizing receding horizon control of nonlinear systems A control lyapunov function approach A. Jadbabaie;J. Yu;J. Hauser
  39. PhD thesis, Califomia Institute Technology Receding Horizon Control of Nonlinear Systems Control Lyapunov Function Approach A. Jadbabaie
  40. AIAA Journal of Guidance and Control v.23 no.3 A receding horizon control Lyapunov function approach to suboptimal regulation of nonlinear systems M. Sznaier;J. Cloutier;R. Hull;D. Jacques;C. Mracek https://doi.org/10.2514/2.4571
  41. Proc. of the IFAC Symposium on Dynamics and Control Chemical Reactors and Batch Processes Optimization in model based control D. Mayne
  42. International Journal of Robust and Nonlinear Control v.13 Suboptimal control of constrained nonlinear systems via receding horizon constrained control Lyapunov functions M. Sznaier;R. Suarez;J. Cloutier https://doi.org/10.1002/rnc.816
  43. Int. J Control v.58 Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty T. H. Yang;E. Polak https://doi.org/10.1080/00207179308923033
  44. Proc. IFA C Symposium Dynamics and Control of Chemical Reactors, Distillation Column and Batch Processes Optimization in model based control D. Q. Mayne
  45. Proc. of the American Control Conference A computationally efficient nonlinear MPC algorithm A. Zheng
  46. Proc. of the American Control Conference Computationally efficient scheduled model predictive control for constrained nonlinear systems with stability guarantees Z. Wan;M. V. Kotharc
  47. Proc. of the American Control Conference Efficient scheduled stabilizing output feedback model predictive control for constrained nonlinear systems Z. Wan;M. V. Kotharc
  48. International Workshop on Nonlinear Predictive Control Improving the efficiency of multiparametric quadratic programming J. Rossiter
  49. International Workshop on Nonlinear Predictive Control A recursive method of optimization for nonlinear predictive control U. Halldorsson;H. Unbehauen
  50. Automatica v.39 Nonlinear model predictive control with polytopic invariant sets M. Cannon;V. Deshmukh;B. Kourvaritakis https://doi.org/10.1016/S0005-1098(03)00128-6
  51. Automatica v.40 Enlargenment of polytopc tenriinal region in NMPC by interpolation and partial invariance M. Cannon;B. Kouvaritakis;V. Deshmukh https://doi.org/10.1016/j.automatica.2003.10.004
  52. Journal of Process Control v.13 A note on stability, robustness and performance of output feedback nonlinear model predictive control L. Imsland;R. Findeisen;E. Bullinger;F. Allgower;B. A. Foss https://doi.org/10.1016/S0959-1524(03)00006-4
  53. International Workshop on Nonlinear Predictive Control Output feedback Model Predictive Control of nonlinear discrete-time systems: regional and global results L. Magni;G. D. Nicolao;R. Scattolini
  54. Journal of Process Control v.13 no.5 Heuristic on-line tuning for nonlinear model predictive controllers using fuzzy logic E. Ali https://doi.org/10.1016/S0959-1524(02)00064-1
  55. IEEE Trans. on Fuzzy Systems v.7 no.3 Model predictive satisficing fuzzy logic control M. Goodrich;W. Stirling;R. Frost https://doi.org/10.1109/91.771087
  56. IEEE Trans. on Systems, Man and Cybernetics v.31 no.1 Model predictive control using fuzzy decision functions J. da Costa Sousa;U. Kaymak https://doi.org/10.1109/3477.907564
  57. Journal of Process Control v.13 no.5 Developing a robust model predictive control architecture through regional knowledge analysis of artificial neural networks P.-F. Tsai;J.-Z. Chu;S.-S. Jang;S.-S. Shieh https://doi.org/10.1016/S0959-1524(02)00067-7
  58. Control Engineering Practice v.11 no.7 Grouped neural network model-predictive control J. Ou;R. R. Rhinehart https://doi.org/10.1016/S0967-0661(02)00184-3
  59. Computers & Chemical Engineering v.26 no.4;5 Automated nonlinear model predictive control using genetic programming B. Grosman;D. R. Lewin https://doi.org/10.1016/S0098-1354(01)00780-3
  60. Chemical Engineering and Processing v.37 no.2 Application of recurrent neural networks in batch reactors: Part II: Nonlinear inverse and predictive control of the heat transfer fluid temperature I. M. Galvan;J. M. Zaldivar https://doi.org/10.1016/S0255-2701(97)00046-9
  61. Computers & Chemical Engineering v.26 no.4;5 Automated nonlinear model predictive control using genetic programming B. Grosman;D. R. Lewin https://doi.org/10.1016/S0098-1354(01)00780-3
  62. Chemical Engineering and Processing v.37 no.2 Application of recurrent neural networks in batch reactors: Part II: Nonlinear inverse and predictive control of the heat transfer fluid temperature I. M. Galvan;J. M. Zaldivar https://doi.org/10.1016/S0255-2701(97)00046-9