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Control Using Logic-Based Switching

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Trends in Control

Abstract

Between the well-studied areas of discontinuous control [1], [2] on the one hand and sampled data control [3] on the other lies the largely unexplored area of logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well {e.g., [4]}. More often than not the predominately logical component within such a system is called a supervisor [5], a mode changer [6], a gain scheduler, or something similar. Within the last decade a number of analytical studies of such systems have emerged, mainly in the area of self-adjusting control [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These studies and others have shown that much can be gained by using logic-based switching together with more familiar techniques in the synthesis of feedback controls. The overall models of systems composed of such logics together with the processes they are intended to control are concrete examples of hybrid dynamical systems [17, 18, 19]. The aim of this paper is to give a brief tutorial review of four different classes of hybrid systems of this type — each consists of a continuous-time process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic.

The author’s research was supported by NSF Grant n. ECS-9206021, AFOSR Grant n. F49620–94–1–0181, and ARO Grant n. DAAH04–95–1–0114

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References

  1. V. I. Utkin. Sliding Modes in Control Optimization. Springer-Verlag, 1992.

    MATH  Google Scholar 

  2. M. I. Zelikin and V. F. Borisov. Theory of Chattering Control. Birkhauser, 1994.

    Book  MATH  Google Scholar 

  3. G. F. Franklin, J. D. Powell, and M. L. Workman. Digital control of Dynamic Systems. Addison-Wesley, 1990.

    MATH  Google Scholar 

  4. C. R. Walli and I. S. Reed. Asynchronous finite-state machines — a novel control system class. AIAA Journal, 7(3):385–393, mar 1969.

    Article  Google Scholar 

  5. C. L. Smith. Digital Computer Process Control. Intext Educational Publishers, 1972.

    Google Scholar 

  6. R. A. Hilhorst. Supervisory Control of Mode-Switch Processes. PhD thesis, University of Twente, 1992.

    Google Scholar 

  7. B. Mårtensson. The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization. Systems and Control Letters, 6(2):87–91, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Fu and B. R. Barmish. Adaptive stabilization of linear systems via switching controls. IEEE Transactions on Automatic Control, pages 1079–1103, December 1986.

    Google Scholar 

  9. S. J. Cusumano and Poola. Adaptive control of uncertain systems: A new approach. In Proceedings of the American Automatic Control Conference, pages 355–359, June 1988.

    Google Scholar 

  10. D. E. Miller. Adaptive Control of Uncertain Systems. PhD thesis, University of Toronto, 1989.

    Google Scholar 

  11. R. H. Middleton, G. C. Goodwin, D. J. Hill, and D. Q. Mayne. Design issues in adaptive control. IEEE Transactions on Automatic Control, 33(1):50–58, jan 1988.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. S. Morse, D. Q. Mayne and G. C. Goodwin. Applications of hysteresis switching in parameter adaptive control. IEEE Transactions on Automatic Control, 37(9):1343–1354, sep 1992.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. R. Weiler and G. C. Goodwin. Hysteresis switching adaptive control of linear multivariable systems. IEEE Transactions on Automatic Control, 39(7): 1369–1375, July 1994.

    Google Scholar 

  14. F. M. Pait and A. S. Morse. A cyclic switching strategy for parameter-adaptive control. IEEE Transactions on Automatic Control, 39(6):1172–1183, jun 1994.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. S. Morse. Dwell-time switching. In Proceedings of the 2nd European Control Conference, pages 176–181, 1993.

    Google Scholar 

  16. K. S. Narendra and J. Balakrishnan. Improving transient response of adaptive control systems using multiple models and switching. Technical report, Yale University, oct 1992.

    Google Scholar 

  17. R. W. Brockett. Hybrid models for motion control systems. In H. L. Ttentleman and J. C. Willems, editors, Essays on Control: Perspectives in the Theory and its Applications, pages 29–54. Birkhäuser, jul 1993.

    Google Scholar 

  18. M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: Background, model, and theory. In Proceedings of the 33rd Conference on Decision and Control, pages 4228–4234. Control Systems Society, IEEE, dec 1994.

    Google Scholar 

  19. R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors. Hybrid Systems, volume 736 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

    Google Scholar 

  20. K. T. Tan. Maximal Output Admissible Sets and the Nonlinear Control of Linear Discrete-Time Systems with State and Control Constraints. PhD thesis, University of Michigan, 1991.

    Google Scholar 

  21. J. P. Hespanha. Stabilization of the nonholonomic integrator via logic-based switching. Technical report, Yale, 1995.

    Google Scholar 

  22. A. S. Morse and F. M. Part. Mimo design models and internal regulators for cyclicly-switched parameter-adaptive control systems. IEEE Transactions on Automatic Control, 39(9): 1809–1818, sept 1994.

    Article  MATH  Google Scholar 

  23. K. S. Narendra and J. Balakrishnan. Adaptive control using multiple models and switching. Technical report, Yale University, jul 1994.

    Google Scholar 

  24. A. S. Morse. Supervisory control of families of linear set-point controllers — part 1: Exact matching, submitted for publication.

    Google Scholar 

  25. A. R. Teel. Global stabilization and tracking for multiple integrators with bounded controls. System and Control Letters, pages 165–171, jan 1992.

    Google Scholar 

  26. H. J. Sussmann, E. D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, pages 2411–2425, dec 1994.

    Google Scholar 

  27. E. G. Gilbert, I. Kolmanovsky, and K. T. Tan. Discrete-time reference governors and the nonlinear control of systems with state and control constraints. Journal of Robust control and Nonlinear Systems, aug 1995. to appear.

    Google Scholar 

  28. P. Kapasouris, M. Athans, and G. Stein. Design of feedback control systems for stable plants with saturating actuators. In Proc. 27th IEEE Conference on Decision and Control, pages 469–479, dec 1988.

    Chapter  Google Scholar 

  29. G. F. Wredenhagen and P. R. Bélanger. Piecewise-linear lq control for systems with input constraints. Automatica, pages 403–416, mar 1994.

    Google Scholar 

  30. E. G. Gilbert and K. T. Tan. Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Transactions on Automatic control, pages 1008–1020, sep 1991.

    Google Scholar 

  31. R. W. Brockett. Asymptotic stability and feedback stabilization. In R. Brockett, R. Millman, and H. Sussmann, editors, Differential Geometric Control theory, pages 181–191, 1983.

    Google Scholar 

  32. R. W. Brockett. Pattern generation and feedback control of nonholonomic systems. In Proceedings of the IEEE Workshop on Mechanics, Holonomy and Control, 1993.

    Google Scholar 

  33. O.J. Sødalen and O. Egeland. Exponential stabilization of nonholonomic chained systems. IEEE Transactions on Automatic Control, 40(1):35–49, 1995.

    Article  Google Scholar 

  34. A. F. Filippov. Differential equations with discontinuous right-hand side. Amer. Math. Soc. Translations, pages 199–231, 1964.

    Google Scholar 

  35. J. Guckenheimer. A robust hybrid stabilization strategy for equilibria. IEEE Transactions on Automatic Control, 40(2):321–325, feb 1995.

    Article  MathSciNet  MATH  Google Scholar 

  36. A. S. Morse. Towards a unified theory of parameter adaptive control — tunability. IEEE Transactions on Automatic Control, 35(9):1002–1012, sep 1990.

    Article  MathSciNet  MATH  Google Scholar 

  37. D. E. Miller and E. J. Davison. An adaptive controller which provides an arbitrary good transient and steady-state response. IEEE Transactions on Automatic Control, 36(1):68–81, jan 1991.

    Article  MathSciNet  MATH  Google Scholar 

  38. D. E. Miller. Adaptive stabilization using a nonlinear time-varying controller. IEEE Transactions on Automatic Control, 39(7):1347–1359, Jul 1994.

    Article  MATH  Google Scholar 

  39. B. Mårtensson and J. W. Polderman. Correction and simplification to “the order of any stabilizing regulator is sufficient a priori information for adaptive stabilization”. Systems and Control Letters, 20:465–470, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  40. S. R. Kulkami and P. J. Ramadge. Model and controller selection policies based on output prediction errors. Technical report, Princeton University, 1995.

    Google Scholar 

  41. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan. Linear matrix Inequalities in Systems and Control Theory. SIAM, 1994.

    Book  Google Scholar 

  42. K. S. Narendra and J. Balakrishnan. Intelligent control using fixed and adaptive models. Technical report, Yale University, oct 1994.

    Google Scholar 

  43. A. S. Morse. Supervisory control of families of linear set-point controllers — part 2: Robustness, submitted for publication.

    Google Scholar 

  44. M. S. Branicky. Stability of switched and hybrid systems. In Proceedings of the 33rd Conference on Decision and Control, pages 3498–3503. Control Systems Society, IEEE, dec 1994.

    Google Scholar 

  45. F. M. Pait. Achieving Tunability in Parameter Adaptive Control. PhD thesis, Yale University, 1993.

    Google Scholar 

  46. A. S. Morse. Logic-based switching and control. In B. A. Francis and A. R. Tannenbaun, editors, Feedback Control, Nonlinear Systems, and Complexity, pages 173–195. Springer-Verlag, 1995.

    Chapter  Google Scholar 

  47. L. Praly and B. E. Ydstie. Adaptive Linear Control: Bounded Solutions and Their Properties, to be published, ≈ 1995.

    Google Scholar 

  48. M. A. Wicks, P. Peleties, and R. A. Decarlo. Construction of piecewise lyapunov functions for stabilizing switched systems. In Proceedings of the 1994 IEEE Conference on Decision and Control, pages 3492–3497, December 1994.

    Chapter  Google Scholar 

  49. K. S. Narendra and J. Balakrishnan. A common lyapunov function for stable lti systems with commuting a-matrices. IEEE Trans. Auto. Control, pages 2469–2470, December 1994.

    Google Scholar 

  50. L. Gurvits. Untitled manuscript, in preparation, jan 1995.

    Google Scholar 

  51. M. Vidyasagar. Nonlinear Systems Analysis. Prentice-Hall, 1993.

    MATH  Google Scholar 

  52. A. P. Molchanov and Ye.S. Pyatnitskiy. Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Systems & Control Letters, pages 59–64, 1989.

    Google Scholar 

  53. Ingrid Daubechies and J. C. Lagarias. Sets of matrices all infinite products of which converge. Linear Algebra and Its Applications, pages 227–263, 1992.

    Google Scholar 

  54. L. Gurvits. Stability of discrete linear inclusion. Linear Algebra and Its Applications, 1995. to appear.

    Google Scholar 

  55. W. A. Sethares, B. D. O. Anderson, and Jr. C. R. Johnson. Adaptive algorithms with filtered regressor and filtered error. Mathematics of control, Signals, and Systems, pages 381–403, feb 1989.

    Google Scholar 

  56. F. M. Pait. On the topologies of spaces on linear dynamical systems commonly employed as models for adaptive and robust control design. In Proceedings of the Third SIAM Conference on Control and Its Applications, 1995.

    Google Scholar 

  57. P. S. Maybeck and D. L. Pogoda. Multiple model adaptive controller for the stol f-15 with sensor/actuator failures. In Proceedings of the 28th IEEE Conference on Decision and Control, pages 1566–1572. IEEE, 1989.

    Chapter  Google Scholar 

  58. A. S. Morse. Towards a unified theory of parameter adaptive control — part 2: Certainty equivalence and implicit tuning. IEEE Transactions on Automatic Control, 37(1):15–29, jan 1992.

    Article  MathSciNet  MATH  Google Scholar 

  59. S. M. Naik, P. R. Kumar, and B. E. Ydstie. Robust continuous-time adaptive control by parameter projection. IEEE Transactions on Automatic Control, 37(2): 182–197, feb 1992.

    Article  MathSciNet  MATH  Google Scholar 

  60. L. Praly. Global stability of direct adaptive control schemes with respect to a group topology. In Adaptive And Learning Systems, pages 5–16, February 1986.

    Google Scholar 

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Authors and Affiliations

  1. Yale University, New Haven, CT, 06520, USA

    A. S. Morse

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  1. A. S. Morse
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  1. Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza”, Via Eudossiana 18, 00184, Roma, Italy

    Alberto Isidori

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Morse, A.S. (1995). Control Using Logic-Based Switching. In: Isidori, A. (eds) Trends in Control. Springer, London. https://doi.org/10.1007/978-1-4471-3061-1_4

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  • DOI: https://doi.org/10.1007/978-1-4471-3061-1_4

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  • Print ISBN: 978-1-4471-3063-5

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