An Inverse Optimal Control Approach for the Nonlinear System Design Using ANN
The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.
[1] Donald E. Kirk, Optimal Control Theory an Introduction, 2nd ed, Dover Publication, Inc., Mineola, N. Y., USA, 2004.
[2] K. S. Narendra and Kannan Parthasarathy, "Identification and Control of Dynamic Systems Using Neural Networks”, IEEE Transactions on Neural Networks, vol. 1, March 1990
[3] Madan M. Gupta and Dandina H. Rao, "Neuro Control Systems – Theorey and Applications, IEEE press – A Select Reprint Volume, 1994.
[4] Mark Hudson Beale, Martin T. Hagan and Howard B. Demuth, "Neural Network Toolbox, User’s Guide, September 2012, The MathWorks, Inc.
[5] Paul J Webrose, "An Overview of Neural Networks for Control” IEEE Trasactions on Control Systems, pp. 40-42, January 1991.
[6] Simon Haykin, Neural Networks – A Comprehensive Foundation, IEEE Press 1994.
[7] Steepen W. Riche, "Steepest Descent Algorithm for Neural Network Controllers and Filters” IEEE Transactions on Neural Networks, vol. 5, no. 2, March 1994.
[8] M. Krstic, I. Kanellakopoulos and P. Kokotovic, "Nonlinear and Adaptive Control Design”, John Wiley and Sons, New York, USA, 1995.
[9] K. D. Do, Z. P. Jiang, and J. Pan, "Simultaneous tracking and stabilization of mobile robots: An adaptive approach”, IEEE Transactions on Automatic Control, vol. 49, pp. 1147–1152, July, 2004.
[10] L. A. Feldkamp, D. V. Prokhorov and T. M. Feldkamp, "Simple and conditioned adaptive behavior from Kalman filter trained recurrent networks”, Neural Networks, vol. 16, pp. 683–689, 2003.
[11] B. S. Park, S. J. Yoo, J. B. Park, and Y. H. Choi, "A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots”, IEEE Transactions on Control System Technology, vol. 18, pp. 1199-1206, September, 2010.
[12] B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ: Prentice-Hall, 1990.
[13] P. J. Moylan and B. D. O. Anderson, "Nonlinear regulator theory and an inverse optimal control problem,” IEEE Trans. Automat. Contr., vol. 18, pp. 460–465, 1973.
[14] R. A. Freeman and P. Kokotovi´c, Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Boston, MA: Birk¨auser, 1996.
[1] Donald E. Kirk, Optimal Control Theory an Introduction, 2nd ed, Dover Publication, Inc., Mineola, N. Y., USA, 2004.
[2] K. S. Narendra and Kannan Parthasarathy, "Identification and Control of Dynamic Systems Using Neural Networks”, IEEE Transactions on Neural Networks, vol. 1, March 1990
[3] Madan M. Gupta and Dandina H. Rao, "Neuro Control Systems – Theorey and Applications, IEEE press – A Select Reprint Volume, 1994.
[4] Mark Hudson Beale, Martin T. Hagan and Howard B. Demuth, "Neural Network Toolbox, User’s Guide, September 2012, The MathWorks, Inc.
[5] Paul J Webrose, "An Overview of Neural Networks for Control” IEEE Trasactions on Control Systems, pp. 40-42, January 1991.
[6] Simon Haykin, Neural Networks – A Comprehensive Foundation, IEEE Press 1994.
[7] Steepen W. Riche, "Steepest Descent Algorithm for Neural Network Controllers and Filters” IEEE Transactions on Neural Networks, vol. 5, no. 2, March 1994.
[8] M. Krstic, I. Kanellakopoulos and P. Kokotovic, "Nonlinear and Adaptive Control Design”, John Wiley and Sons, New York, USA, 1995.
[9] K. D. Do, Z. P. Jiang, and J. Pan, "Simultaneous tracking and stabilization of mobile robots: An adaptive approach”, IEEE Transactions on Automatic Control, vol. 49, pp. 1147–1152, July, 2004.
[10] L. A. Feldkamp, D. V. Prokhorov and T. M. Feldkamp, "Simple and conditioned adaptive behavior from Kalman filter trained recurrent networks”, Neural Networks, vol. 16, pp. 683–689, 2003.
[11] B. S. Park, S. J. Yoo, J. B. Park, and Y. H. Choi, "A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots”, IEEE Transactions on Control System Technology, vol. 18, pp. 1199-1206, September, 2010.
[12] B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ: Prentice-Hall, 1990.
[13] P. J. Moylan and B. D. O. Anderson, "Nonlinear regulator theory and an inverse optimal control problem,” IEEE Trans. Automat. Contr., vol. 18, pp. 460–465, 1973.
[14] R. A. Freeman and P. Kokotovi´c, Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Boston, MA: Birk¨auser, 1996.
@article{"International Journal of Information, Control and Computer Sciences:67405", author = "M. P. Nanda Kumar and K. Dheeraj", title = "An Inverse Optimal Control Approach for the Nonlinear System Design Using ANN", abstract = "The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.
", keywords = "Inverse Optimal Control, Radial basis function neural network, Controller Design.", volume = "8", number = "6", pages = "968-5", }
