Optimal Robust Design of Sliding-mode Control Based on Multi-Objective Particle Swarm Optimization for Chaotic Uncertain Problems
الموضوعات :
Mohammadjavad Mahmoodabadi
1
,
Milad Taherkhorsandi
2
1 - Department of Mechanical Engineering,
Sirjan University of Technology, Sirjan, Iran
2 - Department of Mechanical Engineering,
University of Texas at San Antonio, San Antonio, USA
الکلمات المفتاحية: Robust Control, Multi-objective optimization, Sliding-mode control, particle swarm optimization, Optimal Control, Lorenz chaotic problem,
ملخص المقالة :
The aim of this paper is to present an optimal robust Pareto design of sliding-mode control for chaotic uncertain problems. When designing and applying sliding mode control to challenging dynamic systems, it is crucial to gain optimal control effort and minimum tracking errors, simultaneously. In this regard, multi-objective particle swarm optimization (periodic CDPSO) benefiting from crucial factors such as divergence and convergence operators, the leader selection method, and the adaptive elimination technique is utilized to design the optimal control approach via obtaining the Pareto front of objective functions addressing the trade-off between the states errors and control effort. Afterward, the Pareto front acquired by the periodic CDPSO algorithm is contrasted with those obtained via other prominent algorithms in the literature including Sigma method, Modified NSGAII, and MOGA. Eventually, the numerical results elucidate the effectiveness of the proposed optimal control scheme in terms of optimal control effort and minimum tracking errors.
[1] Gritli, H., Khraief, H., Belghith, S., “Chaos Control in Passive Walking Dynamics of a Compass-gait Model”, Communications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 8, 2013, pp. 2048-2065.
[2] Das, S., Pan, I., Das, S., Gupta, A., “Master-Slave Chaos synchronization via optimal fractional order PID controller with bacterial foraging algorithm”, Nonlinear Dynamics, Vol. 69, No. 4, 2012, pp. 2193-2206.
[3] Sadeghpour, M., Salarieh, H., Alasty, A., “Minimum entropy control of chaos via online particle swarm optimization method”, Applied Mathematical Modelling, Vol. 36, 2012, pp. 3931-3940.
[4] Gholipour, R., Khosravi, A., Mojallali, H., “Multi-objective optimal backstepping controller design for chaos control in a rod-type plasma torch system using Bees algorithm”, Applied Mathematical Modelling, Vol. 39, 2015, pp. 4432-4444.
[5] Wang, X., Deng, L., Zhang, W., “Hopf bifurcation analysis and amplitude control of the modified Lorenz system”, Applied Mathematics and Computations, Vol. 225, 2013, pp. 333-344.
[6] Kim, D., Brent Gillespie, R., Hun Chang, P., “Simple, robust control and synchronization of the Lorenz system”, Nonlinear Dynamics, Vol. 73, No. 1-2, 2013, pp. 971-980.
[7] Li, R.H., Chen, W.S., Li, S., “Finite-time stabilization for hyper-chaotic Lorenz system families via adaptive control”, Applied Mathematical Modelling, Vol. 37, No. 4, 2013, pp. 1966-1972.
[8] Sun, K., Liu, X., Zhu, C., Sprott, J.C., “Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system”, Nonlinear Dynamics, Vol. 69, No. 3, 2012, pp. 1383-1391.
[9] El-Gohary, A., Bukhari, F., “Optimal control of Lorenz system during different time intervals”, Applied Mathematics and Computations, Vol. 144, No. 2, 2003, pp. 337-351.
[10]Tao, C., Yang, C., “Three control strategies for the Lorenz chaotic system”, Chaos, Solitons and Fractals, Vol. 35, No. 5, 2008, pp. 1009-1014.
[11] Zhou, P., Ding, R., “Control and synchronization of the fractional-order lorenz chaotic system via fractional-order derivative”, Mathematical Problems in Engineering, 2012, 14 pages.
[12] Jin, M., Chang, P.H., “Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems”, Chaos, Solitons and Fractals, Vol. 41, No. 5, 2009, pp. 2672-2680.
[13] Wu, Y., Tanner, J.S., “Adaptive control of linear time invariant systems via wavelet network and applications to control Lorenz chaos”, Applied Mathematics and Computations, Vol. 218, No. 1, 2011, pp. 22-31.
[14] Bahrami, M., Ebrahimi, B., Ansarifar, G.R., “Sliding mode observer and control design with adaptive parameter estimation for a supersonic flight vehicle”, International Journal of Aerospace Engineering, 2010, 9 pages.
[15] Chen, M., Mei, R., Jiang, B., “Sliding mode control for a class of uncertain MIMO nonlinear systems with application to near-space vehicles”, Mathematical Problems in Engineering, 2013, 19 pages.
[16] Tavasoli, A., Naraghi, M., “Vehicle sliding mode control with adaptive upper bounds: static versus dynamic allocation to saturated tire forces”, Mathematical Problems in Engineering, 2012, 31 pages.
[17] Tuan, L.A., Lee, S-G., “Sliding mode controls of double-pendulum crane systems”, Journal of Mechanical Science and Technology, Vol. 27, No. 6, 2013, pp.1863-1873.
[18] Richert, D., Masaud, K., Macnab, C.J.B., “Discrete-time weight updates in neural-adaptive control”, Soft Computing, Vol. 17, No. 3, 2013, pp. 431-444.
[19] Mahmoodabadi, M.J., Taherkhorsandi, M., Bagheri, A., “Optimal robust sliding mode tracking control of a biped robot based on ingenious multi-objective PSO”, Neurocomputing, Vol. 124, 2014, pp. 194-209.
[20] Tran, X.T., Kang, H.J., “Adaptive hybrid High-Order terminal sliding mode control of MIMO uncertain nonlinear systems and its application to robot manipulators”, International Journal of Precision Engineering and Manufacturing, Vol. 16, No. 2, 2015, pp. 255-266.
[21]Taherkhorsandi, M., Castillo-Villar, K.K., Mahmoodabadi, M.J., Janaghaei, F., Mortazavi Yazdi, S. M., “Optimal sliding and decoupled sliding mode tracking control by multi-objective particle swarm optimization and genetic algorithms”, Advances and Applications in Sliding Mode Control systems, Studies in Computational Intelligence, Vol. 576, 2015, pp. 43-78.
[22] Liu, D., Guo, W., Wang, W., “Second-order sliding mode tracking control for the piezoelectric actuator with hysteretic nonlinearity”, Journal of Mechanical Science and Technology, Vol. 27, No. 1, 2013, pp. 199-205.
[23] Bisheban, M., Mahmoodabadi, M.J., “Pareto optimal design of decoupled sliding mode control based on a new multi-objective particle swarm optimization algorithm”, Amirkabir International Journal of Science & Research (Modeling, Identification, Simulation & Control). Vol. 45, No. 2, 2013, pp. 31- 40.
[24] Mahmoodabadi, M.J., Taherkhorsandi, M., Talebipour, M., Castillo-Villar, K.K., “Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization”, Transactions of the Institute of Measurement and Control, Vol. 37, No. 4, 2015, pp. 505 - 514.
[25] Andalib Sahnehsaraei, M., Mahmoodabadi, M.J., Taherkhorsandi, M., Castillo-Villar, K.K., Mortazavi Yazdi, S.M., “A hybrid global optimization algorithm: particle swarm optimization in association with a genetic algorithm”, Complex System Modelling and Control Through Intelligent Soft Computations, Studies in Fuzziness and Soft Computing Vol. 319, 2015, pp. 45-86.
[26] Angeline, P.J., “Using selection to improve particle swarm optimization”, In: Proceedings of the IEEE Congress on Evolutionary Computation, Anchorage, 1998, pp. 84-89.
[27] Kennedy, J., Eberhart, R.C., “Particle swarm optimization”, In: Proceedings of the IEEE International Conference on Neural Networks IV, Perth, Australia, 1995, pp. 1942-1948.
[28] Zheng, Z., Wu, C., “Power optimization of gas pipelines via an improved particle swarm optimization algorithm”, Petroleum Sciences, Vol. 9, No. 1, 2012, pp. 89-92.
[29] Garg, H., “Fuzzy multiobjective reliability optimization problem of industrial systems using particle swarm optimization”, International Journal of Industrial Mathematics, 2013, 9 pages.
[30] Lian, Z., “A local and global search combine particle swarm optimization algorithm for job-shop scheduling to minimize makespan”, Discrete Dynamics in Nature and Society, 2010, 11 pages.
[31] Patnaik, S.S., Panda, A.K., “Particle swarm optimization and bacterial foraging optimization techniques for optimal current harmonic mitigation by employing active power filter”, Applied Computational Intelligence and Soft Computing, 2012, 10 pages.
[32]Deepak, B.B.V.L., Parhi, D.R., Raju, B.M.V.A., “Advance particle swarm optimization-based navigational controller for mobile robot”, Arabian Journal of Science and Engineering, Vol. 39, No. 8, 2014, pp. 6477-6487.
[33] Zhan, T.S., Kao, C.C., “Modified PSO method for robust control of 3RPS parallel manipulators”, Mathematical Problems in Engineering, 2010, 25 pages.
[34] Zubair, M., Moinuddin, M., “Joint optimization of microstrip patch antennas using particle swarm optimization for UWB systems”, International Journal of Antennas and Propagation, 2013, 8 pages.
[35] Jin, N., Rahmat-Samii, Y., “Particle swarm optimization for antenna designs in engineering electromagnetic”, Journal of Artificial Evolution and Applications, 2008, 10 pages.
[36] Mahmoodabadi, M.J., Taherkhorsandi, M., Bagheri, A., “Pareto design of state feedback tracking control of a biped robot via multiobjective PSO in comparison with Sigma method and genetic algorithms: modified NSGAII and MATLAB’s Toolbox”, The Scientific World Journal, 2014, 8 pages.
[37]Yildiz, A.R., Solanki, K.N., “Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach”, The International Journal of Advanced Manufacturing and Technology, Vol. 59, No. (1-4), 2012, pp. 367-376.
[38]Geng, B., Mills, J.K., Sun, D., “Combined power management/design optimization for a fuel cell/battery plug-in hybrid electric vehicle using multi-objective particle swarm optimization”, International Journal of Automotive Technology, Vol. 15, No. 4, 2014, pp. 645-654.
[39]Wang, K., Zheng, Y.J., “A new particle swarm optimization algorithm for fuzzy optimization of armored vehicle scheme design”, Applied Intelligence, Vol. 37, No. 4, 2012, pp. 520-526.
[40]Rostami, H., Khaksar Manshad, A., “Application of evolutionary Gaussian processes regression by particle swarm optimization for prediction of dew point pressure in gas condensate reservoirs”, Neural Computing and Applications, Vol. 24, Vol. (3-4), 2014, pp. 705-713.
[41]Ding, S., Jiang, H., Li, J., Tang, G., “Optimization of well placement by combination of a modified particle swarm optimization algorithm and quality map method”, Computational Geosciences, Vol. 18, No. 5, 2014, pp. 747-762.
[42] Eberhart, R.C., Shi, Y., “Comparison between genetic algorithms and particle swarm optimization”, in: Proceedings of the IEEE Congress on Evolutionary Computation, Anchorag, 1998, pp. 611-616.
[43] Hu, X., Eberhart, R.C., “Multi-objective optimization using dynamic neighborhood particle swarm optimization”, In: Proceedings of the IEEE World Congress on Computational Intelligence, 2002, pp. 1677-1681.
[44] Fieldsend, J.E., Singh, S., “A multi-objective algorithm based upon particle swarm optimization and efficient data structure and turbulence”, In: Workshop on Computational Intelligence, 2002, pp. 34-44.
[45] Mostaghim, S., Teich, J., “Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO)”, In: Proceedings of the IEEE Swarm Intelligence Symposium, 2003, pp. 26-33.
[46] Yen, G.G., Leong, W.F., “Dynamic multiple swarms in multi-objective particle swarm optimization”, Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, Vol. 39, No. 4, 2009, pp. 890-911.
[47] Mahmoodabadi, M.J., Bagheri, A., Nariman-zadeh, N., Jamali, A., “A new optimization algorithm based on a combination of particle swarm optimization, convergence and divergence operators for single-objective and multi-objective problems”, Engineering Optimization, Vol. 44, No. 10, 2012, pp. 1167-1186.
[48] Mahmoodabadi, M.J., Bagheri, A., Arabani-Mostaghim, S., Bisheban, M., “Simulation of stability using Java application for Pareto design of controllers based on a new multi-objective particle swarm optimization”, Mathematical and Computer Modelling, Vol. 54, No. 5-6, 2011, pp. 1584-1607.
[49] Wang, Y.Y., Zhang, B.Q., Chen, Y.C., “Robust airfoil optimization based on improved particle swarm optimization method”, Applied Mathematics and Mechanics, Vol. 32, No. 10, 2011, pp. 1245-1254.
[50] Chen, D., Zhao, C., Zhang, H., “An improved cooperative particle swarm optimization and its application”, Neural Computing and Applications, Vol. 20, No. 2, 2011, pp.171-182.
[51] Li, L., Chu, X.S., “An improved particle swarm optimization algorithm with harmony strategy for the location of critical slip surface of slopes”, China Ocean Engineering, Vol. 25, No. 2, 2011, pp. 357-364.
[52] Zhao, J., Han, C., Wei, B., “Binary particle swarm optimization with multiple evolutionary strategies”, Science China Information Sciences, Vol. 55, No. 11, 2012, pp. 2485-2494.
[53] Chen, S., Xu, Z., Tang, Y., “A hybrid clustering algorithm based on fuzzy C-means and improved particle swarm optimization”, Arabian Journal of Science and Engineering, Vol. 39, No. 12, 2014, pp. 8875-8887.
[54] Nickabadi, A., Ebadzadeh, M.M., Safabakhsh, R., “A competitive clustering particle swarm optimizer for dynamic optimization problems”, Swarm Intelligence, Vol. 6, No. 3, 2012, pp. 177-206.
[55] Alfi, A. Modares, H., “System identification and control using adaptive particle swarm optimization”, Applied Mathematical Modelling, Vol. 35, 2011, pp. 1210-1221.
[56] Oliveira, J.B., Boaventura-Cunha, J., Moura Oliveira, P.B., Freire, H., “A swarm intelligence-based tuning method for the sliding mode generalized predictive control”, ISA Transactions, Vol. 53, No. 5, 2014, pp. 1501–1515.
[57] Niknam, T., Khooban, M.H., Kavousifard, A., Soltanpour. M.R., “An optimal type II fuzzy sliding mode control design for a class of nonlinear systems”, Nonlinear Dynamics, Vol. 75, No. 1-2, 2014, pp. 73-83.
[58] Soltanpour, M.R., Khooban, M.H., “A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator”, Nonlinear Dynamics, Vol. 74, No. 1-2, 2013, pp. 467-478.
[59] Taherkhorsandi, M., Mahmoodabadi, M.J., Talebipour, M., Castillo-Villar, K.K., “Pareto design of an adaptive robust hybrid of PID and sliding control for a biped robot via genetic algorithm optimization”, Nonlinear Dynamics, Vol. 79, No. 1, 2015, pp. 251-263.
[60] Jing, J., Wuan, Q.H., “Intelligent sliding mode control algorithm for position tracking servo system”, International Journal of Information Technology, Vol. 12, No. 7, 2006, pp. 57-62.
[61] Lin, W.S., Chen, C.S., “Robust adaptive sliding mode control using fuzzy modeling for a class of uncertain MIMO nonlinear systems”, Control Theory and Applications, Vol. 149, No. 3, 2002, pp. 193-201.
[62] Edwards, C., Spurgeon, S., “Sliding Mode Control: Theory and Applications”, London: Taylor and Francis, 1998, ISBN 0-7484-0601-8.
[63] Guo, H., Lin, S., Liu, J., “A radial basis function sliding mode controller for chaotic Lorenz system”, Physics Letters, Vol. 351, No. 4-5, 2006, pp. 257-261.
[64] Wang, H., Han, Z.Z., Xie, Q.Y., Zhang, W., “Sliding mode control for chaotic systems based on LMI”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, 2009, pp. 1410-1417.
[65] Li, H., Liao, X., Li, C., Li, C., Li, C., “Chaos control and synchronization via a novel chatter free sliding mode control strategy”, Neurocomputing, Vol. 74, No. 17, 2011, pp. 3212-3222.
[66] Bagheri, A., Javadi Moghaddam, J., “Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for a Lorenz chaotic problem”, Expert Systems with Applications, Vol. 36, No. 3, 2009, pp. 6062–6068.
[67] Perruquetti, W., Barbot, J.P., “Sliding Mode Control in Engineering”, Marcel Dekker Hardcover, 2002, ISBN 0-8247-0671-4.
[68] Eberhart, R.C., Kennedy, J., “A new optimizer using particle swarm theory”, In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp. 39-43.
[69] Eberhart, R.C., Dobbins, R., Simpson, P.K., “Computational intelligence PC tools”, Morgan Kaufmann Publishers, 1996.
[70] Engelbrecht, A.P., “Computational intelligence: an introduction”, John Wiley & Sons, 2002.
[71] Engelbrecht, A.P., “Fundamentals of computational swarm intelligence”, John Wiley & Sons 2005.
[72] Ratnaweera, A., Halgamuge, S.K., “Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficient”, IEEE Transactions on Evolutionary Computation, Vol. 8, No. 3, 2004, pp. 240-255.
[73] Utkin, V.I., “Sliding modes and their application in variable structure systems”, Central Books Ltd, 1978.
[74] Toscana, R., “A simple robust PI/PID controller design via numerical optimization approach”, Journal of Process Control Vol. 15, No. 1, 2005, pp. 81-88.
[75]Wolovich, W.A., “Automatic control systems”, USA: Harcourt Brace College Publication Orlando, Saunders College Publishing, 1994.
[76] Atashkari, K., Nariman-Zadeh, N., Golcu, M., Khalkhali, A., Jamali, A., “Modelling and multi-objective optimization of a variable valve-timing spark-ignition engine using polynomial neural networks and evolutionary algorithms”, Energy Conversion and Management, Vol. 48, No. 3, 2007, pp. 1029-1041.
