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Abstract
Introduction
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Control and Systems Engineering

Approximate linearization via feedback — an overview

Profile image of G. GuardabassiG. Guardabassi

2001, Automatica

https://doi.org/10.1016/S0005-1098(00)00117-5
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15 pages

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Abstract

Fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static-state feedback and coordinate transformation, in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback. Main reason for that is the limited applicability of the rigorous methods, and the complexity, sensitivity and design di$culties of the exact linearizing compensators, if any. In the present paper, the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective. Recent works, especially in the area of data-based techniques, are in fact described and related, whenever possible, to fundamental results previously obtained by model-based di!erential geometric methods; this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to "ll visible gaps in this direction. : S 0 0 0 5 -1 0 9 8 ( 0 0 ) 0 0 1 1 7 -5

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References (109)

  1. Abastanotti, D., Colaneri, P., Geromel, J. C., Ghidoni, R., & Guardabassi, G. O. (1989). Nicely nonlinear modelling: A DF approach with application to `linearized process controla. IFAC symposium on nonlinear control systems design. Oxford: Pergamon Press.
  2. Abastanotti, D., Geromel, J. C., Ghidoni, R., & Guardabassi, G. O. (1990). Optimization-based nicely-nonlinear modelling. In H. J. Sebastian, & K. Tammer (Eds.), System modelling and Optimization. Berlin: Springer.
  3. AllgoK wer, F. (1995). Ein Werkzeug zur Analyse und Synthese nich- tlinearer Regelkreise.. In S. Engell (Ed.), Entwurf nichtlinearer Re- gelungen. Munchen: Oldenbourg.
  4. AllgoK wer, F. (1997). Approximate input}output linearization of nonminimum phase nonlinear systems. Fourth European control conference, Brussels, Belgium, paper no. 366, Tu-E-A1.
  5. AllgoK wer, F. A., & Gilles, E. D. (1992). Approximate input/output linearization of nonlinear systems. AIChE annual meeting, Miami, FL. AllgoK wer, F., Rehm, A., & Gilles, E. D. (1994). An engineering perspect- ive on nonlinear H control. 33rd control and decision conference, Lake Buena Vista, FL (pp. 2537}2542).
  6. A s stroK m, K. J., & Wittenmark, B. (1989). Adaptive control. Reading, MA: Addison-Wesley.
  7. Ball, J. A., Helton, J. W., & Walker, M. L. (1993). H control for nonlinear systems with output-feedback. IEEE Transactions on Automatic Control, 38(1), 546}559.
  8. Banaszuk, A., & Hauser, J. (1993). Least squares approximate feedback linearization: A variational approach. 32nd control and decision conference, San Antonio, TX (pp. 2760}2765).
  9. Banaszuk, A., & Hauser, J. (1996). Approximate feedback linearization: A homotopy operator approach. SIAM Journal on Control and Optimization, 34(5), 1533}1554.
  10. Banaszuk, A., S wiech, A., & Hauser, J. (1994). Approximate feed- back linearization: Least squares approximate integrating factors. 33rd control and decision conference, Lake Buena Vista, FL (pp. 1621}1626).
  11. Barbot, J. P., Monaco, S., & Normand-Cyrot, D. (1997). Quadratic forms and approximate feedback linearization in discrete time. International Journal of Control, 67, 567}586.
  12. Barbot, J. P., Monaco, S., & Normand-Cyrot, D. (1999). Discrete-time approximated linearization of SISO systems under output feedback. IEEE Transactions on Automatic Control, 44(9), 1729}1733.
  13. Baumann, W. T., & Rugh, W. J. (1986). Feedback control of nonlinear systems by extended linearization. IEEE Transactions on Automatic Control, 31(1), 40}46.
  14. Bittanti, S., Brasca, C., Corsi, S., Guardabassi, G., Pozzi, M., & Savaresi, S. M. (1996). Approximate linearization of a nonlinear plant: The case of a synchronous generator working in underexcita- tion condition. 13th IFAC world congress, San Francisco, CA (pp. 175}180).
  15. Black, H. S. (1934). Stabilized feedback ampli"ers. Bell System Technical Journal, 13, 1}18. See also: IEEE Spectrum, December 1997, pp. 55}60.
  16. Bonivento, C., Zanasi, R., Sandri, M. (1998). Discrete variable structure integral controllers. Automatica, 34(3), pp. 355}361.
  17. Borto!, S. A., & Spong, M. W. (1992). Pseudolinearization of the acrobot using spline functions. 31st control and decision conference, Tucson, AZ (pp. 593}598).
  18. Braake, H. A. B, van Can, H. J. L., Scherpen, J. M. A., & Verbruggen, H. B. (1998). Control of nonlinear chemical processes using neural models and feedback linearization. Computers and Chemical Engineering, 22, 1113}1127.
  19. Campi, M. C., Lecchini, A., & Savaresi, S. M. (2000). Virtual reference feedback tuning (VRFT): A new direct approach to the design of feedback controllers. 39th IEEE Conference on Design and Control, Sydney.
  20. Castillo, B., Posniak, A., & LoH pez, V. (1993). Approximate tracking near singularities. A di!erential algebraic approach. 32nd control and decision conference, San Antonio, TX (pp. 2778}2782).
  21. Champetier, C., Mouyon, P., & Magni, J.F. (1985). Pseudolinearization of nonlinear systems by dynamic precompensation. 24th control and decision conference, Ft. Lauderdale, FL (pp. 1371}1372).
  22. Champetier, C., Mouyon, P., & Reboulet, C. (1984a). Pseudolineariz- ation of multi-input nonlinear systems. 23rd control and decision conference, Las Vegas, NV (pp. 96}97).
  23. Champetier, C., Reboulet, C., & Mouyon, P. (1984b). A new approach to linearize nonlinear systems: The pseudolinearization. Com- parison with classical methods. 9th IFAC world congress, Budapest (pp. 163}167).
  24. Davison, D. E., & Borto!, S. A. (1994). Enlarge your region of attrac- tion using high-gain feedback. 33rd control and decision conference, Lake Buena Vista, FL (pp. 634}639).
  25. Del Re, L., & Isidori, A. (1995). Performance enhancement of nonlinear drives by feedback linearization of linear-bilinear cascade models. IEEE Transactions on Control Systems Technology, 3(3), 299}308.
  26. Desoer, C. A., & Wang, Y. T. (1980). Foundations of feedback theory for nonlinear dynamical systems. IEEE Transactions on Circuit and Systems, 27(2), 104}123.
  27. Doyle III, F. J., AllgoK wer, F., & Morari, M. (1996). A normal form approach to approximate input}output linearization for maximum- phase nonlinear SISO systems. IEEE Transactions on Automatic Control, 41(2), 305}309.
  28. Fliess, M. (1990). Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Transactions on Automatic Control, 35(9), 994}1001.
  29. Geromel, J. C., & Guardabassi, G. O. (1991). Computer-aided nicely- nonlinear modelling: A set of problem-speci"c MATLAB functions.
  30. In H. A. Barker (Ed.), Proceedings of IFAC symposium on CAD in control systems. Oxford: Pergamon Press.
  31. Guardabassi, G. O. (1992). Nicely-nonlinear modelling and control. In A. Isidori, & T. J. Tarn (Eds.), Systems, models and feedback. Basel: BirkaK user.
  32. Guardabassi, G. O. (1995). Robust stability against mismatched lin- earizing compensation of a class of S.I.S.O. control systems. Third European control conference, Rome, Italy (pp. 2292}2297).
  33. Guardabassi, G. O. (1999). From nonlinearity to nonlinearizability indices. 38th control and decision conference, Phoenix, AZ (pp. 2055}2059).
  34. Guardabassi, G. O., Geromel, J. C., & Jian, X. (1995). Parameter estimation under distributed constraints: two algorithms for convex semi-in"nite quadratic programming problems. In R. Agarwal (Ed.), Recent trends in optimization theory and applications. Singapore: World Scienti"c, pp. 107}121.
  35. Guardabassi, G. O., & Jian, X. (1993). Constrained least-squares identi- "cation of deterministic nicely-nonlinear models. 12th IFAC world congress, Sidney, Australia.
  36. Guardabassi, G. O., Righettini, A., & Ru!oni, I. (1986). Output lineariz- able models and nonlinear control of a distillation column. System Science, 12.
  37. Guardabassi, G. O., & Savaresi, S. M. (1997a). Approximate feedback linearization of discrete-time nonlinear systems using virtual input direct design. Systems & Control Letters, 32, 63}74.
  38. Guardabassi, G. O., & Savaresi, S. M. (1997b). Data-based simulta- neous design of composite feedback}feedforward controllers: a virtual input direct design approach. Fourth European control conference, Brussels, Belgium, paper no. 111, We-A-F6.
  39. Guardabassi, G. O, & Savaresi, S. M. (1997c). Identi"cation of single- input multi-output nicely-nonlinear models. 11th IFAC symposium on system identixcation, Fukuoka, Japan (pp. 697}702).
  40. Guardabassi, G. O., & Savaresi, S. M. (2000). Virtual reference direct design method: An o!-line approach to data-based control system design. IEEE Transactions on Automatic Control, 45(5), 954}959.
  41. Guzzella, L., & Isidori, A. (1993). On approximate linearization of nonlinear control systems. International Journal of Robust and Nonlinear Control, 3, 261}276.
  42. Gwo, E. C., & Hauser, J. (1993a). A numerical approach for approxim- ate feedback linearization. American control conference, San Francisco, CA (pp. 1495}1499).
  43. Gwo, E. C., & Hauser, J. (1993b). Approximate feedback linearization: An ¸ numerical approach. 32nd control and decision conference, San Antonio, TX (pp. 2772}2777).
  44. Haber, R. (1985). Nonlinearity test for dynamic processes. IFAC sympo- sium on identixcation and system parameter estimation, New York (pp. 409}413).
  45. Hauser, J. (1990). Nonlinear control via uniform system approximation. 29th control and decision conference, Honolulu, Hawaii (pp. 792}797).
  46. Hauser, J. (1991). Nonlinear control via uniform system approximation. Systems & Control Letters, 17, 145}154.
  47. Hauser, J., & Banaszuk, A. (1997). Approximate feedback linearization around a trajectory: Application to trajectory planning. 36th control and decision conference, San Diego, CA (pp. 7}11).
  48. Hauser, J., Sastry, S., & Kokotovic, P. (1989). Nonlinear control via approximate input}output linearization: The ball and beam example. 28th control and decision conference, Tampa, FL (pp. 1987}1993).
  49. Hauser, J., Sastry, S., & Kokotovic, P. (1992). Nonlinear control via approximate input}output linearization: The ball and beam example. IEEE Transactions on Automatic Control, 37(3), 392}398.
  50. Hauser, J., Sastry, S., & Meyer, G. (1992). Nonlinear control design for slightly nonminimum phase systems: Application to VSTOL air- craft. Automatica, 24(4), 665}679.
  51. Hung, J. Y, Gao, W., & Hung, J. C. (1993). Variable structure control: A survey. IEEE Transactions on Industrial Electronics, 40(1), 2}21. Hunt, L. R., Su, R., & Meyer, G. (1983). Global transformations of nonlinear systems. IEEE Transactions on Automatic Control, 28, 24}31.
  52. Ichikawa, Y., & Sawa, T. (1992). Neural network application for direct feedback controllers. IEEE Transactions on Neural Networs, 3(2), 224}231.
  53. Isermann, R., Ernst, S., & Nelles, O. (1997). Identi"cation with dynamic neural networks * architectures, comparisons, applications. 11th IFAC symposium on system identixcation, Fukuoka, Japan (pp. 997}1022).
  54. Isidori, A., & Astol", A. (1992). Disturbance attenuation and H con- trol via measurement feedback in nonlinear systems. IEEE Transac- tions on Automatic Control, 37.
  55. Isidori, A., & Ruberti, A. (1984). On the synthesis of linear input}output responses for nonlinear systems. Systems & Control Letters, 4, 17}22.
  56. Jakubczyk, B., & Respondek, W. (1980). On linearization of control systems. Bulletindel+ Academic Polonaise Sciences Serie Sciences Mathematiques, 28, 517}522.
  57. Kang, W. (1994). Approximate linearization of nonlinear control sys- tems. Systems & Control Letters, 23, 43}52.
  58. Kaya, C. Y. (1999). Linearization of control systems and the swing-out. 14th IFAC world congress, Beijing, China, vol. E (pp. 509}514).
  59. Krener, A. J. (1973). On the equivalence of control systems and the linearization of nonlinear systems. SIAM Journal of Control, 11, 670}676.
  60. Krener, A. J. (1984). Approximate linearization by state feedback and coordinate change. Systems & Control Letters, 5, 181}185.
  61. Krener, A. J., Karahan, S., & Hubbard, M. (1988). Approximate normal forms of nonlinear systems. 27th control and decision conference, TX (pp. 1223}1229).
  62. Krener, A. J., Karahan, S., Hubbard, M., & Frezza, F. (1987). Higher order linear approximations to nonlinear control systems. 26th control and decision conference, Los Angeles, CA (pp. 519}523).
  63. Kucera, V. (1979). Discrete linear control * the polynomial equation approach. New York: Wiley.
  64. Landau, Y. D. (1979). Adaptive control: The model reference approach. New York: Marcel-Dekker.
  65. Lawrence, D. A. (1995). A general approach to input}output pseudo- linearization for nonlinear systems. 34th control and decision confer- ence, New Orleans, LA (pp. 613}618).
  66. Lawrence, D. A. (1999). Approximate model matching for nonlinear systems. 38th control and decision conference, Phoenix, AZ (pp. 720}725).
  67. Lawrence, D. A., & Rugh, W. J. (1994). Input}output pseudo-lineariz- ation for nonlinear systems. IEEE Transactions on Automatic Control, 39(11), 2207}2217.
  68. Lee, H. G., & Marcus, S. J. (1986). Approximate and local linearizability of nonlinear discrete-time systems. International Journal of Control, 44(4), 1103}1124.
  69. Levin, A. U., & Narendra, K. S. (1996). Control of nonlinear dynamical systems using neural networks * Part II: Observability, identi"ca- tion, and control. IEEE Transactions on Neural Networks, 7(1), 30}42.
  70. Lindskog, P., & Ljung, L. (1997). Ensuring certain physical properties in black-box models by applying fuzzy techniques. 11th IFAC sym- posium on system identixcation, Fukuoka, Japan (pp. 721}726).
  71. Lu, W. M., & Doyle, J. C. (1994). H control of nonlinear systems via output-feedback: Controller parametrization. IEEE Transactions on Automatic Control, 39.
  72. Marino, R., Respondek, W., & van der Shaft, A. J. (1989). Almost disturbance decoupling for SISO nonlinear systems. IEEE Transac- tions on Automatic Control, 34(2), 1013}1017.
  73. Menon, P. K., & Yousefpor, M. (1996). Design a nonlinear autopilots for high angle of attack missiles. AIAA guidance, navigation and control conference, San Diego, CA (pp. 1}18).
  74. Nam, K., Arapostathis, A., & Lee, S. (1993). Some numerical aspects of approximate linearization of single-input nonlinear systems. Inter- national Journal of Control, 57(2), 463}472.
  75. Nam, K., Lee, S., & Won, S. (1993). A local stabilizing control scheme using an approximate feedback linearization. 32nd control and deci- sion conference, San Antonio, TX (pp. 2783}2784).
  76. Nam, K., Lee, S., & Won, S. (1994). A local stabilizing control scheme using an approximate feedback linearization. IEEE Transactions on Automatic Control, 39(11), 2311}2314.
  77. Narendra, K. S., & Mukhopadhyay, K. (1995). Adaptive control using neural networks and approximate models. American control confer- ence, Seattle, WA (pp. 355}359).
  78. Narendra, K. S., & Parthasarathy, X. (1990). Identi"cation and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks 1(1), 4}27.
  79. Nijmeijer, H., & Savaresi, S. M. (1998). On approximate model-refer- ence control of SISO discrete-time nonlinear systems. Automatica, 34(10), 1261}1266.
  80. Nikolaou, M. (1993). When is nonlinear dynamic modeling necessary? American control conference, San Francisco, CA (pp. 910}913).
  81. Ogunnaike, B. A., Pearson, R. K., & Doyle III, F. J. (1993). Chemical process characterization: With applications in the rational selection of control strategies. 2nd European control conference, Groningen, The Netherlands (pp. 1067}1071).
  82. Oishi, M., & Tomlin, C. (1999). Switched nonlinear control of a VSTOL aircraft. 38th control and decision conference, Phoenix, AZ (pp. 2685}2690).
  83. Pearson, R. K., & Ogunnaike, B. A. (1993). Application of coherence analysis in linear and nonlinear input/output model identi"cation. AICHE annual meeting, St. Louis, MO.
  84. Reboulet, C., & Champetier, C. (1984). A new method for linearizing nonlinear systems: the pseudolinearization. International Journal of Control, 40, 631}638.
  85. Rugh, W. J. (1984). Design of nonlinear compensators for nonlinear systems by an extended linearization technique. 23rd control and decision conference, Las Vegas, NV (pp. 69}73).
  86. Rugh, W. J. (1986). An extended linearization approach to nonlinear system inversion. IEEE Transactions on Automatic Control, 31(8), 725}733.
  87. Savaresi, S. M. (1997). Parametric identixcation and control of nonlinear systems. Ph.D. thesis, Politecnico di Milano, Italy (in Italian).
  88. Savaresi, S. M., & Guardabassi, G. O. (1997a). Approximate I/O feed- back linearization of discrete-time nonlinear systems via virtual input direct design. Automatica, 34(6), 715}722.
  89. Savaresi, S. M., & Guardabassi, G. O. (1997b). Invertible nonlinear parametric functions for systems identi"cation and control. Interna- tional Journal of Robust and Nonlinear Control, 8, 741}762.
  90. Savaresi, S. M., & Guardabassi, G. O. (1997c). The invertibility con- straint for nonlinear parametric functions. 11th IFAC symposium on system identixcation, Fukuoka, Japan (pp. 1237}1242).
  91. Savaresi, S. M., & Guardabassi, G. O. (1997d). Approximate feedback linearization of nonlinear systems: a data-based direct design approach. 36th control and decision conference, San Diego, CA (pp. 18}23).
  92. Savaresi, S. M., Guardabassi, G. O., Brasca, C., Corsi, S., Pozzi, M. (1997). Improving the dynamics of a synchronous generator by nonlinear stabilizers: A virtual reference direct design approach. IEEE-ASME conference on control applications, Hartford, CT (pp. 571}576).
  93. Savaresi, S. M., Nijmeijer, H., Guardabassi, G. O. (2000). On the design of approximate nonlinear parametric controllers. International Jour- nal of Robust and Nonlinear Control, 10, 137}155.
  94. Sayid, M. A., & Naylor, P. A. (1994). A novel nonlinearity measure. IEE conference control +94 (pp. 1368}1373).
  95. SjoK berg, J., Hjalmarsson, H., & Ljung, L. (1994). Neural network in system identi"cation. IFAC symposium on system identixcation, Copenhagen, vol. 2, pp. 49}72.
  96. Sourlas, D. D., & Manousiouthakis, V. (1998). On the computation of the nonlinearity measure. 37th control and decision conference, Tampa, FL (pp. 1434}1439).
  97. Spall, J. C., & Cristion, J. A. (1993). Model-free control of general discrete-time systems. 32nd control and decision conference, San Antonio, TX (pp. 2792}2797).
  98. Stack, A. J., & Doyle III, F. J. (1995). A measure for control relevant nonlinearity. American control conference, Seattle (pp. 2200}2204).
  99. Stack, A. J., & Doyle III, F. J. (1997). Application of a control- law nonlinearity measure to the chemical reactor analysis. Process Systems Engineering, 43(2), 425}439.
  100. Su, R. (1982). On the linear equivalents of nonlinear systems. Systems & Control Letters, 2, 48}52.
  101. Takagi, T., & Sugeno, M. (1985). Fuzzy identi"cation of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15, 116}132.
  102. Utkin, V. I. (1992). Sliding modes in control optimization. Berlin: Spring- er.
  103. Vadigepalli, R., & Doyle, F. J. (1999). A simulation study of the nonlinear dynamic characteristic of a local cardiac re#ex in the rat. American control conference, San Diego, CA (pp. 1248}1252).
  104. Van der Schaft, A. J., & Ball, J. A. (1994). Nonlinear inner}outer factorization. 33rd control and decision conference, Lake Buena Vista, FL (pp. 2549}2554).
  105. Wang, J., & Rugh, W. J. (1987a). Feedback linearization families for nonlinear systems. IEEE Transactions on Automatic Control, 32(10), 935}940.
  106. Wang, J., & Rugh, W. J. (1987b). Parameterized linear systems and linearization families for nonlinear systems. IEEE Transactions on Circuits and Systems, 34(6), 650}657.
  107. Wang, J., & Rugh, W. J. (1989). On the pseudo-linearization problem for nonlinear systems. Systems & Control Letters, 12, 161}167.
  108. Zhong, R., Chang, B. C., Yeh, H. H., & Banda, S. S. (1995). An approximate I/O linearization via nonlinear H model-matching. 34th control and decision conference, New Orleans, LA (pp. 345}346). Guido O. Guardabassi was born on Febru- ary 12, 1940, in Piacenza, Italy. He re- ceived the Dr. Eng. degree in Electronics from the Politecnico di Milano in 1964., where he became Assistant, Associate (`Libero docentea) and Full Professor of Automatic Control in 1967, 1971, and 1975, rspectively. He is the author of many papers in the area of systems and control, especially: complex systems analysis, linear multivariable control, optimal periodic control and periodic systems analysis.
  109. More recently, his research interests focus on direct data-based control system design (nicely-nonlinear modelling, virtual input method, in- verse controller method), and their application to real industrial prob- lems. He is or has been on the editorial board of three national (Alta Frequenza, La Meccanica Italiana, Ricerche di Automatica) and "ve international (Automatica, Information and Decision Technologies, Optimal Control Applications and Methods, Studies in Informatics and Control, Systems Science) scienti"c journals. Dr. Guardabassi has long been active in IFAC in many capacities including Chairman of the System Engineering Committee, Chairman of the Publications Com- mittee, and Member of the Council. He is a Fellow of IEEE. Sergio M. Savaresi was born in Manerbio, Italy, on September 21, 1968. He received the Doctor Degree (Laurea) in Electrical Engineering from the Politecnico di Milano in 1992, and the Ph.D. in Systems and Control Engineering in 1997. In 1998 he worked at McKinsey & Co., and since the end of 1998 he is an Assistant Professor at the Politecnico di Milano. His main interests are in the areas of data analysis and system identi"cation, nonlinear con- trol theory, and control applications.

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Rendiconti del Seminario Matematico e Fisico di Milano, 1996

The possibility of using feedback to achieve or to enhance system linearity is well known to control engineers since decades ago. A few major breakthroughs, made possible by the application of differential geometric tools to control theoretic issues, have revamped a new interest in all facets of the problem, including the search, the analysis and the computation of suitable approximate solutions. In the present paper, recent developments and new trends in the field are shortly reviewed, with special attention paid to some research issues currently addressed by the authors. Though primarily meant for learned mathematically oriented readers, the presentation focuses on ideas and concepts more than on their most general and mathematically rigorous formulations. On the other hand, it does not assume familiarity with advanced control theory nor modern control technology.

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Exact linearization of nonlinear systems with outputs
Tzyh-jong T J T J Tarn

Mathematical Systems Theory, 1988

This paper discusses the problem of using feedback and coordinates transformation in order to transform a given nonlinear system with outputs into a controllable and observable linear one. We discuss separately the effect of change of coordinates and, successively, the effect of both change of coordinates and feedback transformation. One of the main results of the paper is to show what extra conditions are needed, in addition to those required for input-output-wise linearization, in order to achieve full linearity of both state-space equations and output map.

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Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
Gilberto Gonzalez Avalos

Symmetry

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

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Nonlinear Controllers Based on Feedback Linearization Technique
Mohsen Ghribi

2015

Abstract:- This paper describes new software (NLSoft) developed for the design of nonlinear controllers based on feedback linearization technique. NLSoft is a software package containing several symbolic manipulation modules including differential geometric tools for the design and simulation of control systems. NLSoft presents a user-friendly graphical user interface (GUI) as well as a new and powerful module allowing the calculation time of linearizing control laws considering several Digital Signal Processors (DSPs) characteristics. These facilitate the real-time implementation of the control system. NLSoft is validated considering two illustrated examples. 1.

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Feedback linearization of possibly non-smooth systems
Alexey Zhirabok

Proceedings of the Estonian Academy of Sciences, 2017

The algebraic approach known as functions' algebra is used to develop the necessary and sufficient conditions for the existence of state transformation and static state feedback that linearize the system equations. The advantage of this method is that it allows considering also non-smooth systems. The main object in functions' algebra is the set of vector functions, divided into equivalence classes, which form a lattice. Both discrete-and continuous-time cases are considered. The solutions to the feedback linearization problem are expressed in terms of a finite sequence of vector functions, which contain all the independent functions having certain relative degrees. The theoretical results are illustrated by numerous examples.

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