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Journal articles on the topic 'Geometric nonlinear control'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Alvarez, Jesus, Teresa Lopez, and Eduardo Hernandez. "Robust Geometric Nonlinear Control of Process Systems." IFAC Proceedings Volumes 33, no. 10 (June 2000): 395–400. http://dx.doi.org/10.1016/s1474-6670(17)38572-5.

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2

Brockett, Roger. "The early days of geometric nonlinear control." Automatica 50, no. 9 (September 2014): 2203–24. http://dx.doi.org/10.1016/j.automatica.2014.06.010.

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3

MAIDI, Ahmed, and Jean Pierre CORRIOU. "Boundary Geometric Control of Nonlinear Diffusion Systems." IFAC Proceedings Volumes 46, no. 26 (2013): 49–54. http://dx.doi.org/10.3182/20130925-3-fr-4043.00016.

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4

Wu, Shu Jing, Da Zhong Wang, and Shigenori Okubo. "Control for Nonlinear Chemical System." Key Engineering Materials 467-469 (February 2011): 1450–55. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.1450.

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In this paper, we propose a new design of the feedback control of state vector for the plants with polynomial dynamics. A genetic algorithm is employed to find suitable gain, and algebraic geometric concept is used to simplify the design. Finally, an example is given to illustrate the effectiveness of the proposed method.

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5

MIROSHNIK, Iliya V. "PARTIAL STABILIZATION AND GEOMETRIC PROBLEMS OF NONLINEAR CONTROL." IFAC Proceedings Volumes 35, no. 1 (2002): 151–56. http://dx.doi.org/10.3182/20020721-6-es-1901.00275.

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6

Elkin, V. I. "Geometric Theory of Reduction of Nonlinear Control Systems." Computational Mathematics and Mathematical Physics 58, no. 2 (February 2018): 155–58. http://dx.doi.org/10.1134/s0965542518020045.

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7

Bell, D. "Algebraic and geometric methods in nonlinear control theory." Automatica 24, no. 4 (July 1988): 586–87. http://dx.doi.org/10.1016/0005-1098(88)90105-7.

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8

Burstein, Gabriel. "Algebraic and geometric methods in nonlinear control theory." Acta Applicandae Mathematicae 11, no. 2 (February 1988): 177–91. http://dx.doi.org/10.1007/bf00047286.

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9

Kravaris, Costas, and Jeffrey C. Kantor. "Geometric methods for nonlinear process control. 1. Background." Industrial & Engineering Chemistry Research 29, no. 12 (December 1990): 2295–310. http://dx.doi.org/10.1021/ie00108a001.

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10

Chen, Yahao, and Witold Respondek. "Geometric analysis of nonlinear differential-algebraic equations via nonlinear control theory." Journal of Differential Equations 314 (March 2022): 161–200. http://dx.doi.org/10.1016/j.jde.2022.01.008.

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11

Schlacher, Kurt, Andreas Kugi, and Werner Haas. "Geometric Control of a Class Of Nonlinear Descriptor Systems." IFAC Proceedings Volumes 31, no. 17 (July 1998): 379–84. http://dx.doi.org/10.1016/s1474-6670(17)40365-x.

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12

Tadé, M. O., and K. M. Kam. "Differential Geometric Nonlinear Control on an Operator Training System." IFAC Proceedings Volumes 36, no. 11 (June 2003): 231–36. http://dx.doi.org/10.1016/s1474-6670(17)35668-9.

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13

Marino, R., and P. V. Kokotovic. "A Geometric Approach to Nonlinear Singularly Perturbed Control Systems." IFAC Proceedings Volumes 20, no. 5 (July 1987): 169–74. http://dx.doi.org/10.1016/s1474-6670(17)55081-8.

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14

Marino, R., and P. V. Kokotovic. "A geometric approach to nonlinear singularly perturbed control systems." Automatica 24, no. 1 (January 1988): 31–41. http://dx.doi.org/10.1016/0005-1098(88)90005-2.

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15

Ruiz, A. C., and H. Nijmeijer. "Nonlinear Control Problems and Systems Approximations: a Geometric Approach." IFAC Proceedings Volumes 25, no. 13 (June 1992): 315–20. http://dx.doi.org/10.1016/s1474-6670(17)52300-9.

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16

Fliess, M., J. Lévine, P. Martin, and P. Rouchon. "On a new differential geometric setting in nonlinear control." Journal of Mathematical Sciences 83, no. 4 (February 1997): 524–30. http://dx.doi.org/10.1007/bf02434981.

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17

Kravaris, Costas, and Jeffrey C. Kantor. "Geometric methods for nonlinear process control. 2. Controller synthesis." Industrial & Engineering Chemistry Research 29, no. 12 (December 1990): 2310–23. http://dx.doi.org/10.1021/ie00108a002.

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18

Kulhavý, Rudolf. "Recursive nonlinear estimation: A geometric approach." Automatica 26, no. 3 (May 1990): 545–55. http://dx.doi.org/10.1016/0005-1098(90)90025-d.

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19

Xiaohua Xia and Jiangfeng Zhang. "Geometric Steady States of Nonlinear Systems." IEEE Transactions on Automatic Control 55, no. 6 (June 2010): 1448–54. http://dx.doi.org/10.1109/tac.2010.2044261.

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20

Sakamoto, Noboru, and Enrique Zuazua. "The turnpike property in nonlinear optimal control—A geometric approach." Automatica 134 (December 2021): 109939. http://dx.doi.org/10.1016/j.automatica.2021.109939.

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21

IZAWA, Yoshiaki, and Kyojiro HAKOMORI. "Control of Nonlinear System with Hysteresis by Riemannian Geometric Approach." Transactions of the Society of Instrument and Control Engineers 33, no. 12 (1997): 1124–30. http://dx.doi.org/10.9746/sicetr1965.33.1124.

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22

Bezick, Scott, Ilan Rusnak, and W. Steven Gray. "Guidance of a homing missile via nonlinear geometric control methods." Journal of Guidance, Control, and Dynamics 18, no. 3 (May 1995): 441–48. http://dx.doi.org/10.2514/3.21407.

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23

Hassan, Ahmed M., and Haithem E. Taha. "Geometric control formulation and nonlinear controllability of airplane flight dynamics." Nonlinear Dynamics 88, no. 4 (March 1, 2017): 2651–69. http://dx.doi.org/10.1007/s11071-017-3401-9.

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24

Lin, Zhongwei, Jizhen Liu, Weihai Zhang, and Yuguang Niu. "A geometric approach toH∞control of nonlinear Markovian jump systems." International Journal of Control 87, no. 9 (March 11, 2014): 1833–45. http://dx.doi.org/10.1080/00207179.2014.891292.

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25

McCaffrey, D., and S. P. Banks. "Geometric existence theory for the control-affine nonlinear optimal regulator." Journal of Mathematical Analysis and Applications 305, no. 1 (May 2005): 380–90. http://dx.doi.org/10.1016/j.jmaa.2004.12.017.

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26

Alvarez, Jesús, Fernando Zaldo, and Salvador Padilla. "Integration of Process and Control Designs by Nonlinear Geometric Methods." IFAC Proceedings Volumes 28, no. 9 (June 1995): 363–68. http://dx.doi.org/10.1016/s1474-6670(17)47064-9.

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27

Álvarez, Jesús, and Carlos Fernández. "Geometric estimation of nonlinear process systems." Journal of Process Control 19, no. 2 (February 2009): 247–60. http://dx.doi.org/10.1016/j.jprocont.2008.04.017.

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28

Valpiani, James M., and Philip L. Palmer. "Nonlinear Geometric Estimation for Satellite Attitude." Journal of Guidance, Control, and Dynamics 31, no. 4 (July 2008): 835–48. http://dx.doi.org/10.2514/1.32715.

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29

Mujumdar, Anusha, and Radhakant Padhi. "Reactive Collision Avoidance of Using Nonlinear Geometric and Differential Geometric Guidance." Journal of Guidance, Control, and Dynamics 34, no. 1 (January 2011): 303–11. http://dx.doi.org/10.2514/1.50923.

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30

Aeyels, Dirk. "Global Controllability for Smooth Nonlinear Systems: A Geometric Approach." SIAM Journal on Control and Optimization 23, no. 3 (May 1985): 452–65. http://dx.doi.org/10.1137/0323029.

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31

Shiryayeva, O. I., and L. K. Abzhanova. "Synthesis of nonlinear multiply control system based on geometric approach summary." Journal of Mathematics, Mechanics and Computer Science 92, no. 4 (2017): 109–17. http://dx.doi.org/10.26577/jmmcs-2017-4-459.

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32

Krstic, Miroslav, and Rafael Vazquez. "NONLINEAR CONTROL OF PDES: ARE FEEDBACK LINEARIZATION AND GEOMETRIC METHODS APPLICABLE?" IFAC Proceedings Volumes 40, no. 12 (2007): 20–27. http://dx.doi.org/10.3182/20070822-3-za-2920.00004.

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33

IZAWA, Yoshiaki, and Kyojiro HAKOMORI. "Nonlinear Control of a Double-Effect Evaporator by Riemannian Geometric Approach." Transactions of the Society of Instrument and Control Engineers 32, no. 2 (1996): 197–206. http://dx.doi.org/10.9746/sicetr1965.32.197.

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34

Gil, Iván D., Julio C. Vargas, and Jean P. Corriou. "Nonlinear Geometric Temperature Control of a Vinyl Acetate Emulsion Polymerization Reactor." Industrial & Engineering Chemistry Research 53, no. 18 (December 31, 2013): 7397–408. http://dx.doi.org/10.1021/ie402296j.

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35

Kam, Kiew M., Moses O. Tadé, Gade P. Rangaiah, and Yu C. Tian. "Strategies for Enhancing Geometric Nonlinear Control of an Industrial Evaporator System." Industrial & Engineering Chemistry Research 40, no. 2 (January 2001): 656–67. http://dx.doi.org/10.1021/ie000205g.

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36

Kennedy, D., D. Miller, and Victor Quintana. "A nonlinear geometric approach to power system excitation control and stabilization." International Journal of Electrical Power & Energy Systems 20, no. 8 (November 1998): 501–15. http://dx.doi.org/10.1016/s0142-0615(98)00023-4.

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37

Wu, Wei, and Ming-Yuan Huang. "Nonlinear inferential control for an exothermic packed-bed reactor: geometric approaches." Chemical Engineering Science 58, no. 10 (May 2003): 2023–34. http://dx.doi.org/10.1016/s0009-2509(03)00051-4.

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38

Chiasson, J. "Nonlinear differential-geometric techniques for control of a series DC motor." IEEE Transactions on Control Systems Technology 2, no. 1 (March 1994): 35–42. http://dx.doi.org/10.1109/87.273108.

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39

Raab, Sadia, Hacene Habbi, and Ahmed Maidi. "Late‐lumping fuzzy boundary geometric control of nonlinear partial differential systems." International Journal of Robust and Nonlinear Control 30, no. 16 (August 15, 2020): 6473–501. http://dx.doi.org/10.1002/rnc.5108.

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40

Chen, Yahao, and Stephan Trenn. "On geometric and differentiation index of nonlinear differential-algebraic equations." IFAC-PapersOnLine 54, no. 9 (2021): 186–91. http://dx.doi.org/10.1016/j.ifacol.2021.06.075.

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41

Echeverría-Enríquez, A., J. Marín-Solano, M. C. Muñoz-Lecanda, and N. Román-Roy. "Geometric reduction in optimal control theory with symmetries." Reports on Mathematical Physics 52, no. 1 (August 2003): 89–113. http://dx.doi.org/10.1016/s0034-4877(03)90006-1.

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42

Zhou, Yi, Yuan-Qi Li, Zu-Yan Shen, and Ying-Ying Zhang. "Corotational Formulation for Geometric Nonlinear Analysis of Shell Structures by ANDES Elements." International Journal of Structural Stability and Dynamics 16, no. 03 (March 3, 2016): 1450103. http://dx.doi.org/10.1142/s021945541450103x.

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The corotational (CR) kinematic description was a recent method for formulation of geometric nonlinear structural problems. Based on the consistent symmetrizable equilibrated (CSE) CR formulation, a linear triangular flat shell element with three translational and three rotational degrees of freedom (DOFs) at each of the three nodes was derived by the assumed natural deviatoric strain (ANDES) formulation, which can be used to the geometric nonlinear analysis of shell structures with large rotations and small strains. By taking variations of the internal energy with respect to nodal freedoms, the equations for the CR nonlinear finite element, including the tangent stiffness matrix and the internal force vector in the global coordinate system, were derived. The nonlinear equations were solved by using the generalized displacement control (GDC) method. It was shown through numerical examples that combing CR formulation and ANDES elements can accurately solve complex geometric nonlinear problems with large body motions. As revealed by the efficiency and reliability of the ANDES elements in tracing the nonlinear structural load–deflection response, it is demonstrated that some membrane elements and plate elements give better performance in the geometric nonlinear analysis of shell structures.

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43

Coates, Erlend M., and Thor I. Fossen. "Geometric Reduced-Attitude Control of Fixed-Wing UAVs." Applied Sciences 11, no. 7 (April 1, 2021): 3147. http://dx.doi.org/10.3390/app11073147.

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This paper presents nonlinear, singularity-free autopilot designs for multivariable reduced-attitude control of fixed-wing aircraft. To control roll and pitch angles, we employ vector coordinates constrained to the unit two-sphere and that are independent of the yaw/heading angle. The angular velocity projected onto this vector is enforced to satisfy the coordinated-turn equation. We exploit model structure in the design and prove almost global asymptotic stability using Lyapunov-based tools. Slowly-varying aerodynamic disturbances are compensated for using adaptive backstepping. To emphasize the practical application of our result, we also establish the ultimate boundedness of the solutions under a simplified controller that only depends on rough estimates of the control-effectiveness matrix. The controller design can be used with state-of-the-art guidance systems for fixed-wing unmanned aerial vehicles (UAVs) and is implemented in the open-source autopilot ArduPilot for validation through realistic software-in-the-loop (SITL) simulations.

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44

Liu, Xiang, Guoping Cai, Fujun Peng, and Hua Zhang. "Nonlinear vibration control of a membrane antenna structure." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 9 (August 14, 2018): 3273–85. http://dx.doi.org/10.1177/0954410018794321.

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In this paper, the active control of nonlinear vibration of a membrane antenna structure is investigated. Considering the geometric nonlinearity of large amplitude vibration of the membrane, the von Karman type geometrical nonlinear strain–displacement relationship is employed in this paper. Then, a nonlinear dynamic model of the membrane antenna structure is established by using the finite element method. It is assumed that the amplitude of vibration of the structure is relatively small when the controller in on, and then a [Formula: see text] robust controller is developed to control the undesired nonlinear vibration of the membrane antenna structure based on the linearized model of the structure. Active control of both the free vibration and forced vibration of the structure are investigated. Numerical simulations are presented to study the nonlinearity of the large amplitude vibration of the structure and the effectiveness of the presented controller.

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45

Kolar, Bernd, Markus Schöberl, and Johannes Diwold. "Differential–geometric decomposition of flat nonlinear discrete-time systems." Automatica 132 (October 2021): 109828. http://dx.doi.org/10.1016/j.automatica.2021.109828.

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46

Sass, B., and Z. Toroczkai. "Continuous extension of the geometric control method." Journal of Physics A: Mathematical and General 29, no. 13 (July 7, 1996): 3545–57. http://dx.doi.org/10.1088/0305-4470/29/13/023.

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47

Sarychev, Andrey V. "Higher-order techniques for some problems of nonlinear control." Mathematical Problems in Engineering 8, no. 4-5 (2002): 413–38. http://dx.doi.org/10.1080/10241230306725.

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A natural first step when dealing with a nonlinear problem is an application of some version oflinearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.

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48

Wang, Yebin, and Kenji Utsunomiya. "From acceleration-based semi-active vibration reduction control to functional observer design." at - Automatisierungstechnik 66, no. 3 (March 26, 2018): 234–45. http://dx.doi.org/10.1515/auto-2017-0064.

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Abstract This work investigates a functional estimation problem for single input single output linear and nonlinear systems, motivated by its enabling role in acceleration-based semi-active control. Solvability of a linear functional estimation problem is studied from a geometric approach, where the functional dynamics are derived, decomposed, and transformed to expose structural properties. This approach is extended to solve a challenging nonlinear functional observer problem, combining with the exact error linearization. Existence conditions of nonlinear functional observers are established. Simulation verifies existence conditions and demonstrates the effectiveness of the proposed functional observer designs.

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49

Wijnbergen, Paul, Mark Jeeninga, and Bart Besselink. "Nonlinear spacing policies for vehicle platoons: A geometric approach to decentralized control." Systems & Control Letters 153 (July 2021): 104954. http://dx.doi.org/10.1016/j.sysconle.2021.104954.

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50

Lee, Dae Young, Rohit Gupta, Uroš V. Kalabić, Stefano Di Cairano, Anthony M. Bloch, James W. Cutler, and Ilya V. Kolmanovsky. "Geometric Mechanics Based Nonlinear Model Predictive Spacecraft Attitude Control with Reaction Wheels." Journal of Guidance, Control, and Dynamics 40, no. 2 (February 2017): 309–19. http://dx.doi.org/10.2514/1.g001923.

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