Optimal Control of Switched Systems Based on Continuous Hopfield Neural Network
In this paper, a new approach is proposed for the optimal control problem of switched systems. This approach, based on Continuous Hopfield Neural Network (CHNN), has been used to find the optimal switching instants to minimize a performance index that is defined over a finite time horizon and transformed into the energy function of CHNN. The switching instants present the output vector of the neurons of CHNN. As a result, solving a dynamic optimization problem is equivalent to operating associated CHNN from its initial state to the terminal state. Based on the stable output vector of CHNN, which represents the optimal switching instants, we can find the optimal control sequence. As CHNN works in parallel and as it is of real-time characteristic, the present method is easier to satisfy the requirement of real-time control and is promising in application. We demonstrate via numerical examples the effectiveness of the proposed approach where the results are compared to those obtained by conventional methods, such as simple gradient and Quasi-Newton methods, and other non-conventional methods such as the Particle Swarm Optimization (PSO). By applying the proposed algorithm on a hydraulic system, it seems a general solution for the optimal control problem of switching instants, for a number of reasons; first, no regularity in the performance function is required; second, it is valid for many dynamics, and finally, it provides a global optimum.
Copyright © 2014 Praise Worthy Prize - All rights reserved.
X. Xu and P.J. Antsaklis, Optimal Control of Switching Systems Based on Parameterization of the Switching Instants, Trans. Automat. Contr., vol. 49, no. 1. IEEE, 2004.
X. Xu and P.J. Antsaklis, Optimal control of switched systems: new results and open problems. Proc. 28-30 June 2000 Amer. Control Conf., vol. 4. IEEE, Chicago 2683–2687, 2000.
X. Xu and P.J. Antsaklis, A Dynamic Programming Approach for Optimal Control of Switched Systems, Proceedings of the 39th IEEE Conference on Decision and Control Sydney, Australia 2000.
N. Majdoub, A. Sakly, M. Sakly, M. Benrejeb, Ant Colony-Based Optimization of Switching Instants for Autonomous Switched Systems, (2010) International Review of Automatic Control (IREACO), 3 (1), pp. 24-31.
T. Bak, J. Bendtsen, and A.P. Ravn, Hybrid control design for a wheeled mobile robot, Hybrid Systems: Computation and Control. O. Maler, Amir Pnueli (Eds), no. 2623 in LNCS,50-65, Spinger 2003.
A. Back, J. Guckenheirmer, and M. Myers, A Dynamical Simulation Facility for Hybrid Systems, Hybrid Systems, Lecture Notes in Computer Science (LNCS), vol. 736. Springer New York 255-267, 1993.
C. Tomlin, G.J. Pappas, J. Lygeros, D.N. Godbole, and S. Sastry, Hybrid control models of next generation air traffic management, Hybrid Systems IV, no 1273 in LNCS, Springer, 1997.
A.S. Matveev and A.V. Savkin, Qualitative Theory of hybrid dynamical systems, Birk- hÄauser, Boston 2000.
A. Bemporad, P. Borodani, and M. Manneli, Hybrid control of an automotive robotized gearbox for reduction of consumptions and emissions, Hybrid Systems: Computation and Control,O. Maler, Amir Pnueli (Eds), vol. 2623 in LNCS 81-96, Spinger 2003.
A. Bemporad, F. Borrelli, and M. Morari, Optimal controllers for hybrid systems: stability and piecewise linear explicit, IEEE Conf. Decision Control, Sydney 12-151810–1815, 2000.
X. Xu and P.J. Antsaklis, Optimal control of switched systems via nonlinear optimization based on direct differentiations of value functions, Int. J. Control., vol. 75, no. 16/17 1406–1426, 2002.
X. Xu and P.J. Antsaklis, Results and perspectives on computational methods for optimal control of switched systems, Hybrid Systems: Computation and Control, vol. 2623 (HSCC2003) Dame, 2001.
X. Xu, Analysis and Design of Switched Systems, PhD Thesis, University of Notre Dame, 2001.
J. Hopfield and D. Tank, Neural computation of decision in optimization problems, Bio. Cybernet, vol. 52, pp. 141–152, 1985.
L. Chua and G. N. Lin, Nonlinear programming without computation, IEEE Trans. Circuits Syst., vol. 31, pp. 182–188,1984.
D. Ramirez, M. R. Arahal, and E. F. Camacho, Min-max predictive control of a heat exchanger using a neural network solver, IEEE transactions on control systems technology, vol. 12, no. 05, pp. 776–786,2004.
N. Majdoub, A. Sakly, and M. Benrejeb, Hybrid Approach for Optimal Control Problem of Switched Systems, IEEE, 978-1-4244-6588, 2010.
LI IMing-ai, RUAN Xiao-gang, Optimal Control with Continuous Hopfield Neural Network, International Conference on Robotics, Intelligent Systems and Signal Processing, Changsha, China - October 2003.
T. Coleman and Y. Li, On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds, Mathematical Programming, vol. 67, no. 2,pp. 189–224, 1994.
T. Coleman and Y. Li, An interior, trust region approach for nonlinear minimization subject to bounds, SIAM Journal on Optimization, vol. 6, pp. 418–445, 1996.
- There are currently no refbacks.
Please send any question about this web site to firstname.lastname@example.org
Copyright © 2005-2019 Praise Worthy Prize