Details

PDF BIBTEX RIS

Title

Experimental verification of H∞ control with examples of the movement of a wheeled robot

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2021

Volume

69

Issue

6

Affiliation

Hendzel, Zenon : Department of Applied Mechanics and Robotics, Faculty of Mechanical Engineering and Aeronautics, Rzeszów University of Technology, ul. Powstańców Warszawy 12, 35-959 Rzeszów, Poland ; Penar, Paweł : Department of Applied Mechanics and Robotics, Faculty of Mechanical Engineering and Aeronautics, Rzeszów University of Technology, ul. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Authors

Hendzel, Zenon ; Penar, Paweł

Keywords

differential game ; H∞ control ; wheeled mobile robot

Divisions of PAS

Nauki Techniczne

Coverage

e139390

Bibliography

  1.  B. Kovács, G. Szayer, F. Tajti, M. Burdelis, and P. Korondi, “A novel potential field method for path planning of mobile robots by adapting animal motion attributes,” Rob. Auton. Syst., vol. 82, pp. 24–34, 2016, doi: 10.1016/j.robot.2016.04.007.
  2.  A. Pandey, “Mobile Robot Navigation and Obstacle Avoidance Techniques: A Review,” Int. Robotics Autom. J., vol. 2, no. 3, pp. 96–105, 2017, doi: 10.15406/iratj.2017.02.00023.
  3.  R.C. Arkin, Behavior-based robotics. The MIT Press, 1998.
  4.  M. Szuster and Z. Hendzel, Intelligent Optimal Adaptive Control for Mechatronic Systems. Springer, 2018.
  5.  M.J. Giergiel, Z. Hendzel, and W. Żylski, Modeling and control of mobile wheeled robots. PWN, 2013, [in Polish].
  6.  P. Bozek, Y.L. Karavaev, A.A. Ardentov, and K.S. Yefremov, “Neural network control of a wheeled mobile robot based on optimal tra- jectories,” Int. J. Adv. Rob. Syst., vol. 17, no. 2, pp. 1–10, 2020, doi: 10.1177/1729881420916077.
  7.  P. Gierlak and Z. Hendzel, Control of wheeled and manipulation robots. Publishing House Rzeszow Univ. of Technology, 2011, [in Polish].
  8.  B. Kiumarsi, K.G. Vamvoudakis, H. Modares, and F.L. Lewis, “Optimal and Autonomous Control Using Reinforcement Learning: A Survey,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 6, pp. 2042–2062, 2018.
  9.  F.L. Lewis, D. Vrabie, and V.L. Syrmos, Optimal control. John Wiley & Sons, 2012.
  10.  K.G. Vamvoudakis and F.L. Lewis, “Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem,” Automatica, vol. 46, no. 5, pp. 878–888, 2010.
  11.  F.-Y.Wang, H. Zhang, and D. Liu, “Adaptive Dynamic Programming: An Introduction,” IEEE Comput. Intell. Mag., vol. 4, no.  May, pp. 39–47, 2009.
  12.  A.G. Barto, W. Powell, J. Si, and D.C. Wunsch, Handbook of learning and approximate dynamic programming. Wiley-IEEE Press, 2004.
  13.  D. Liu, Q. Wei, D. Wang, X. Yang, and H. Li, Adaptive Dynamic Programming with Applications in Optimal Control. Springer, Advances in Industrial Control, 2017.
  14.  A.J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control. Springer International Publishing, 2017.
  15.  B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control. Springer-Verlag London, 2007.
  16.  A.W. Starr and Y.C. Ho, “Nonzero-sum differential games,” J. Optim. Theory Appl., vol. 3, no. 3, pp. 184–206, 1969.
  17.  M. Abu-Khalaf, J. Huang, and F.L. Lewis, Nonlinear H2 Hinf Constrained Feedbacka Control. Springer-Verlag London, 2006.
  18.  D. Liu, H. Li, and D. Wang, “Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm,” Neurocomputing, vol. 110, pp.  92–100, 2013.
  19.  C. Qin, H. Zhang, Y. Wang, and Y. Luo, “Neural network-based online Hinf control for discrete-time affine nonlinear system using adaptive dynamic programming,” Neurocomputing, vol. 198, pp.  91–99, 2016.
  20.  D. Liu, H. Li, and D. Wang, “Hinf control of unknown discretetime nonlinear systems with control constraints using adaptive dynamic programming,” in The 2012 International Joint Conference on Neural Networks (IJCNN). IEEE, 2012, pp. 1–6.
  21.  Z. Hendzel and P. Penar, “Zero-Sum Differential Game in Wheeled Mobile Robot Control,” Int. Conf. Mechatron., vol. 934, pp. 151–161, 2017.
  22.  Z. Hendzel, “Optimality in Control for Wheeled Robot,” Adv Intell. Syst. Comput.: Autom. 2018, vol. 743, pp. 431–440, 2018.
  23.  Y. Fu and T. Chai, “Online solution of two-player zero-sum games for continuous-time nonlinear systems with completely unknown dynamics,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 12, pp. 2577–2587, 2015.
  24.  K.G. Vamvoudakis and F.L. Lewis, “Online solution of nonlinear two-player zero-sum games using synchronous policy iteration,” Int. Robust. Nonlinear Control, vol. 22, pp. 1460–1483, 2012.
  25.  S. Yasini, A. Karimpour, M.-B. Naghibi Sistani, and H. Modares, “Online concurrent reinforcement learning algorithm to solve two-player zero-sum games for partially unknown nonlinear continuous-time systems,” Int. J. Adapt Control Signal Process., vol. 29, no. 4, pp. 473– 493, 2015.
  26.  B. Luo, H.-N. Wu, and T. Huang, “Off-policy reinforcement learning for Hinf control design,” IEEE Trans. Cybern., vol. 45, no. 1, pp. 65–76, 2014.
  27.  H.-N. Wu and B. Luo, “Neural Network Based Online Simultaneous Policy Update Algorithm for Solving the HJI Equation in Nonlinear Hinf Control,” IEEE Trans. Neural Netw. Learn. Syst., vol.  23, no. 12, pp. 1884–1895, 2012.
  28.  Y. Zhu, D. Zhao, and X. Li, “Iterative adaptive dynamic programming for solving unknown nonlinear zero-sum game based on online data,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 3, pp. 714–725, 2016.
  29.  J. Zhao, M. Gan, and C. Zhang, “Event-triggered Hinf optimal control for continuous-time nonlinear systems using neurodynamic pro- gramming,” Neurocomputing, vol. 360, pp. 14–24, 2019.
  30.  B. Dong, T. An, F. Zhou, S. Wang, Y. Jiang, K. Liu, F. Liu, H. Lu, and Y. Li, “Decentralized Robust Optimal Control for Modular Robot Manipulators Based on Zero-Sum Game with ADP,” in International Symposium on Neural Networks. Springer, 2019, pp. 3–14.
  31.  H. Modares, F.L. Lewis, and Z.-P. Jiang, “Hinf Tracking Control of Completely Unknown Continuous-Time Systems via Off-Policy Reinforcement Learning,” IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 10, pp. 2550–2562, 2015.
  32.  J.C. Willems, “Dissipative Dynamical Systems. Part I: General Theory,” Arch. Ration. Mech. Anal., vol. 45, pp.  321–351, 1972.
  33.  D.J. Hill and P.J. Moylan, “Dissipative Dynamical Systems: Basic Input-Output and State Properties,” J. Franklin Inst., vol. 305, no.  5, pp. 327–357, 1980.
  34.  A.J. van der Schaft, “L2-gain Analysis of Nonlinear Systems and Nonlinear State Feedback Hinf Control,” IEEE Trans. Autom. Control, vol. 37, no. 6, pp. 770–784, 1992.
  35.  S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnam, Linear Matrix Inequalities in System and Control Theory. SIAM studies in applied mathematics: 15, 1994.
  36.  S. Yasini, M.B.N. Sistani, and A. Karimpour, “Approximate dynamic programming for two-player zero-sum game related to Hinf control of unknown nonlinear continuous-time systems,” Int. J. Control Autom. Syst., vol. 13, no. 1, pp. 99–109, 2014.
  37.  W. Zylski, Kinematics and dynamics of mobile wheeled robots. Publishing House Rzeszow Univ. of Technology, 1996, [in Polish].
  38.  J. Giergiel and W. Żylski, “Description of motion of a mobile robot by Maggie’s equations,” J. Theor. Appl. Mech., vol. 43, no. 3, pp. 511–521, 2005.
  39.  J. Garca De Jaln, A. Callejo, and A.F. Hidalgo, “Efficient solution of Maggi’s equations,” J. Comput. Nonlinear Dyn., vol. 7, no. 2, 2012, doi: 10.1115/1.4005238.
  40.  A. Kurdila, J.G. Papastavridis, and M.P. Kamat, “Role of Maggi’s equations in computational methods for constrained multibody systems,” J. Guidance Control Dyn., vol. 13, no. 1, pp. 113–120, 1990, doi: 10.2514/3.20524.
  41.  DS1103, Hardware Installation and Configuration. dSpace, 2009.
  42.  ActiveMedia, Pioneer 2DX Operation Manual Peterborough, 1999.

Date

04.11.2021

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.139390
×