Stability of infinite dimensional interconnected systems with impulsive and stochastic disturbances. (English) Zbl 1406.93081

Summary: Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.


93B12 Variable structure systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C73 Perturbations in control/observation systems
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[1] Gong, X.; Hou, Z.-C.; Zhao, C.-J.; Bai, Y.; Tian, Y.-T., Adaptive backstepping sliding mode trajectory tracking control for a quad-rotor, International Journal of Automation and Computing, 9, 5, 555-560 (2012)
[2] Chen, Y.; Hoo, K. A., Stability analysis for closed-loop management of a reservoir based on identification of reduced-order nonlinear model, Systems Science and Control Engineering: An Open Access Journal, 1, 1, 12-19 (2013)
[3] Dong, H.; Wang, Z.; Ho, D. W. C.; Gao, H., Robust \(H_\infty\) filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case, IEEE Transactions on Signal Processing, 59, 7, 3048-3057 (2011) · Zbl 1391.93234
[4] Dong, H. L.; Wang, Z. D.; Gao, H. J., Distributed filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transaction on Industrial Electronics, 60, 10, 4665-4672 (2013)
[5] Dong, H.; Wang, Z.; Gao, H., Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities, IEEE Transactions on Circuits and Systems: I: Regular Papers, 59, 10, 2354-2362 (2012) · Zbl 1468.94903
[6] Gao, J.-G.; Deng, F.-Q.; Zhang, C.-K.; Sun, Y.-F., Asymptotic stability of stochastic impulsive system via comparison approach, Proceedings of the 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR ’10)
[7] Yao, F.; Deng, F., Comparison principle and stability of impulsive stochastic functional differential systems in terms of two measures, Proceedings of the 8th IEEE International Conference on Control and Automation (ICCA ’10)
[8] Liu, B., Stability of solutions for stochastic impulsive systems via comparison approach, IEEE Transactions on Automatic Control, 53, 9, 2128-2133 (2008) · Zbl 1367.93523
[9] Li, C.; Sun, J.; Sun, R., Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects, Journal of the Franklin Institute. Engineering and Applied Mathematics, 347, 7, 1186-1198 (2010) · Zbl 1207.34104
[10] Yang, J.; Zhong, S.; Luo, W., Mean square stability analysis of impulsive stochastic differential equations with delays, Journal of Computational and Applied Mathematics, 216, 2, 474-483 (2008) · Zbl 1142.93035
[11] Pan, L.; Cao, J., Exponential stability of impulsive stochastic functional differential equations, Journal of Mathematical Analysis and Applications, 382, 2, 672-685 (2011) · Zbl 1222.60043
[12] Shi, J.-Z.; Zhang, J.-Y., String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay, International Journal of Systems Science: Principles and Applications of Systems and Integration, 45, 5, 1035-1041 (2014) · Zbl 1284.93243
[13] Xu, X. H.; Zhang, J. Y.; Tang, L., String exponential stability with mode constraint of stochastic vehicle following systems, ASME Journal of Dynamic Systems, Measurement, and Control, 135, 6 (2013)
[14] Shi, J. Z.; Zhang, J. Y.; Tang, J. Y., The global exponential stability of a class of linear stochastic interconnected large-scale systems, Proceedings of the International Conference on Computer and Computational Intelligence, Nanning
[15] Zhou, J.; Peng, H., Range policy of adaptive cruise control vehicles for improved flow stability and string stability, IEEE Transactions on Intelligent Transportation Systems, 6, 2, 229-237 (2005)
[16] Schultz, A. C.; Parker, L. E., Multi-Robot Systems: From Swarms to Intelligent AuTomata (2002), Dordrecht, The Netherlands: Kluwer Academic, Dordrecht, The Netherlands
[17] Pant, A.; Seiler, P.; Hedrick, K., Mesh stability of look-ahead interconnected systems, IEEE Transactions on Automatic Control, 47, 2, 403-407 (2002) · Zbl 1364.93577
[18] Zhang, J.; Suda, Y.; Iwasa, T.; Komine, H., Vector Liapunov function approach to longitudinal control of vehicles in a platoon, JSME International Journal C: Mechanical Systems, Machine Elements and Manufacturing, 47, 2, 653-658 (2004)
[19] Socha, L., Stochastic stability of interconnected string systems, Chaos, Solitons and Fractals, 19, 4, 949-955 (2004) · Zbl 1053.60063
[20] Zhou, J.; Lu, J.; Peng, H., Vehicle stabilization in response to exogenous impulsive disturbances to the vehicle body, Proceedings of the American Control Conference (ACC ’09)
[21] Aracil, J.; Heredia, G.; Ollero, A., Global stability analysis of fuzzy path tracking using frequency response, Engineering Applications of Artificial Intelligence, 13, 2, 109-119 (2000)
[22] Swaroop, D.; Karl Hedrick, J.; Choi, S. B., Direct adaptive longitudinal control of vehicle platoons, IEEE Transactions on Vehicular Technology, 50, 1, 150-161 (2001)
[23] Lee, G. D.; Kim, S. W., A longitudinal control system for a platoon of vehicles using a fuzzy-sliding mode algorithm, Mechatronics, 12, 1, 97-118 (2002)
[24] Shi, J. Z.; Zhang, J. Y.; Xu, X. H., String stability of stochastic interconnected systems with time delays, Acta Automatica Sinica: Zidonghua Xuebao, 36, 12, 1744-1751 (2010) · Zbl 1240.93356
[25] Khasminski, R. Z., Stochastic Stability of Differential Equations. Stochastic Stability of Differential Equations, Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, 7 (1980), Groningen, The Netherlands: Sijthoff & Noordhoff, Groningen, The Netherlands
[26] Niu, Y.; Ho, D. W. C., Robust observer design for Itô stochastic time-delay systems via sliding mode control, Systems & Control Letters, 55, 10, 781-793 (2006) · Zbl 1100.93047
[27] Higham, D. J., An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Review, 43, 3, 525-546 (2001) · Zbl 0979.65007
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