# American Institute of Mathematical Sciences

• Previous Article
Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint
• JIMO Home
• This Issue
• Next Article
Construction schedule optimization for high arch dams based on real-time interactive simulation
October  2015, 11(4): 1343-1354. doi: 10.3934/jimo.2015.11.1343

## Optimal tracking control for networked control systems with random time delays and packet dropouts

 1 School of Computer Science, Xi'an Shiyou University, Xi'an, 710065, China 2 Department of Automation, Northwestern Polytechnical University, Xi'an, 710072, China, China

Received  October 2012 Revised  February 2015 Published  March 2015

This paper studies the problem of optimal output tracking control for networked control system with uncertain time delays and packet dropouts. Active time-varying sampling period strategy is proposed to ensure the random variable time delays always shorter than one sampling period. Hybrid driven modes are adopted by sensor to solve the issues of long time delay and packet dropout. By using augmentation approach, the tracking problem of this formulated within-one-step delayed discrete-time system is transformed into a general problem of non-delayed state linear quadratic regulator. A “gridding” approach is introduced to guarantee the realization of optimal output feedback control law by the solution of a series of Riccati matrix equations from an offline database that is constructed by different combination of time delays and packet dropouts. Simulation results demonstrate the effectiveness of the optimal tracking control law.
Citation: Ying Wu, Zhaohui Yuan, Yanpeng Wu. Optimal tracking control for networked control systems with random time delays and packet dropouts. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1343-1354. doi: 10.3934/jimo.2015.11.1343
##### References:
 [1] N. Duan and X. J. Xie, Further results on output-feedback stabilization for a class of stochastic nonlinear systems,, IEEE Transactions on Automatic Control, 56 (2011), 1208.  doi: 10.1109/TAC.2011.2107112.  Google Scholar [2] D. M. Dawson, et al., Tracking control of rigid-link electrically-driven robot manipulators,, International Journal of Control, 56 (1992), 991.  doi: 10.1080/00207179208934354.  Google Scholar [3] H. J. Gao and T. W. Chen, Network-based $H_\infty$ output tracking control,, IEEE Transactions on Automatic Control, 53 (2008), 655.  doi: 10.1109/TAC.2008.919850.  Google Scholar [4] L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays,, Journal of Industrial and Management Optimization, 10 (2014), 413.   Google Scholar [5] S. Y. Han, et al., Near-Optimal Tracking Control for Discrete-time Systems with Delayed Input,, International Journal of Control Automation and Systems, 8 (2010), 1330.  doi: 10.1007/s12555-010-0619-4.  Google Scholar [6] C. J. Hou, Y. P. Chen and Z. L. Lu, Superconvergence property of finite element methods for parabolic optimal control problems,, Journal of Industrial and Management Optimization, 7 (2011), 927.  doi: 10.3934/jimo.2011.7.927.  Google Scholar [7] K. Ji and W. J. Kim, Stabilization of networked control system with time delays and data-packet losses,, European Journal of Control, 13 (2007), 343.  doi: 10.3166/ejc.13.343-350.  Google Scholar [8] B. Jayawardhana and G. Weiss, Tracking and disturbance rejection for fully actuated mechanical systems,, Automatica, 44 (2008), 2863.  doi: 10.1016/j.automatica.2008.03.030.  Google Scholar [9] S. Liu, L. Xie and H. S. Zhang, Linear quadratic tracking problem for discrete-time systems with multiple delays in single input channel,, International Journal of Robust and Nonlinear Control, 20 (2010), 1379.  doi: 10.1002/rnc.1520.  Google Scholar [10] M. Mauder, Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot,, Automatica, 44 (2008), 2588.  doi: 10.1016/j.automatica.2008.02.012.  Google Scholar [11] A. Naskali and A. Onat, Random network delay in model based predictive networked control systems,, in Proc. $6^{nd}$ WSEAS Int. Conf. Appl. Comput. Sci., 1 (2006), 199.   Google Scholar [12] A. Onat, et al., Control over imperfect networks: Model-based predictive networked control systems,, IEEE Transactions on Industrial Electronics, 58 (2011), 905.  doi: 10.1109/TIE.2010.2051932.  Google Scholar [13] A. Onat and E. Parlakay, Implementation of networked predictive control system,, in Proc. 9th Real-Time Linux Workshop, 1 (2007), 85.   Google Scholar [14] T. Suzuki, et al., Controllability and stabilizability of a networked control system with periodic communication constraints,, Systems & Control Letters, 60 (2011), 977.  doi: 10.1016/j.sysconle.2011.08.004.  Google Scholar [15] Y. Shi and B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains,, IEEE Transactions on Automatic Control, 54 (2009), 1668.  doi: 10.1109/TAC.2009.2020638.  Google Scholar [16] A. Sala, Computer control under time-varying sampling period: An LMI gridding approach,, Automatica, 41 (2005), 2077.  doi: 10.1016/j.automatica.2005.05.017.  Google Scholar [17] B. O. S. Teixeira, et al., Spacecraft tracking using sampled-data Kalman filters - An illustrative application of extended and unscented estimators,, IEEE Control Systems Magazine, 28 (2008), 78.  doi: 10.1109/MCS.2008.923231.  Google Scholar [18] Y. H. Wang, Z. M. Wang and Y. F. Zheng, On the model-based networked control for singularly perturbed systems,, International Journal of Robust and Nonlinear Control, 6 (2008), 153.  doi: 10.1007/s11768-008-6152-9.  Google Scholar [19] J. Wu and T. W. Chen, Design of networked control systems with packet dropouts,, IEEE Transactions on Automatic Control, 52 (2007), 1314.  doi: 10.1109/TAC.2007.900839.  Google Scholar [20] H. H. Wang, Optimal tracking for Discrete-Time Systems with Input Delays,, Proceedings of the 2008 Chinese Control and Decision Conference, (2008), 4033.   Google Scholar [21] Y. L. Wang and G. H. Yang, Output tracking control for networked control systems with time delay and packet dropout,, International Journal of Control, 81 (2008), 1709.  doi: 10.1080/00207170701836944.  Google Scholar [22] Y. Wang and G. Yang, Output tracking control for discrete-time networked control systems,, IEEE American Control Conference, (2009), 5109.  doi: 10.1109/ACC.2009.5159974.  Google Scholar [23] D. Wu, J. Wu and S. Chen, Robust $H_\infty$ control for networked control systems with uncertainties and multiple-packet transmission,, IET Control Theory Appl., 4 (2010), 701.  doi: 10.1049/iet-cta.2009.0090.  Google Scholar [24] Y. L. Wang and G. H. Yang, Output tracking control for continuous-time networked control systems with communication constraints,, Proc. of the American Control Conference, (2009), 531.  doi: 10.1109/ACC.2009.5159975.  Google Scholar [25] H. H. Wang and G. Y. Tang, Observer-based optimal output tracking for discrete-time systems with multiple state and input delays,, International Journal of Control Automation and Systems, 7 (2009), 57.  doi: 10.1007/s12555-009-0108-9.  Google Scholar [26] H. W. Yu, X. M. Zhang, G. P. Lu and Y. F. Zheng, On model based networked control for singularly perturbed systems with nonlinear uncertainties,, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, (2009), 684.  doi: 10.1109/CDC.2009.5400103.  Google Scholar [27] D. Yue, Q. L. Han and J. Lam, Network-based robust $H_\infty$ control of systems with uncertainty,, Automatica, 41 (2005), 999.  doi: 10.1016/j.automatica.2004.12.011.  Google Scholar [28] X. M. Zhang, et al., Stochastic stability of networked control systems with network-induced delay and data dropout,, in Proceedings of the 45th Ieee Conference on Decision and Control, 14 (2006), 5006.  doi: 10.1109/CDC.2006.376970.  Google Scholar [29] H. G. Zhang, J. Yang and C. Y. Su, T-S fuzzy-model-based robust $H_\infty$ design for networked control systems with uncertainties,, IEEE Trans. Ind. Inf., 3 (2007), 289.   Google Scholar [30] Q. Zhang, et al., An Enhanced LMI Approach for Mixed $H_2/H_\infty$ Flight Tracking Control,, Chinese Journal of Aeronautics, 24 (2011), 324.   Google Scholar [31] H. B. Zeng, et al., Absolute stability and stabilization for Lurie networked control systems,, International Journal of Robust and Nonlinear Control, 21 (2011), 1667.  doi: 10.1002/rnc.1658.  Google Scholar

show all references

##### References:
 [1] N. Duan and X. J. Xie, Further results on output-feedback stabilization for a class of stochastic nonlinear systems,, IEEE Transactions on Automatic Control, 56 (2011), 1208.  doi: 10.1109/TAC.2011.2107112.  Google Scholar [2] D. M. Dawson, et al., Tracking control of rigid-link electrically-driven robot manipulators,, International Journal of Control, 56 (1992), 991.  doi: 10.1080/00207179208934354.  Google Scholar [3] H. J. Gao and T. W. Chen, Network-based $H_\infty$ output tracking control,, IEEE Transactions on Automatic Control, 53 (2008), 655.  doi: 10.1109/TAC.2008.919850.  Google Scholar [4] L. Gollmann and H. Maurer, Theory and applications of optimal control problems with multiple time-delays,, Journal of Industrial and Management Optimization, 10 (2014), 413.   Google Scholar [5] S. Y. Han, et al., Near-Optimal Tracking Control for Discrete-time Systems with Delayed Input,, International Journal of Control Automation and Systems, 8 (2010), 1330.  doi: 10.1007/s12555-010-0619-4.  Google Scholar [6] C. J. Hou, Y. P. Chen and Z. L. Lu, Superconvergence property of finite element methods for parabolic optimal control problems,, Journal of Industrial and Management Optimization, 7 (2011), 927.  doi: 10.3934/jimo.2011.7.927.  Google Scholar [7] K. Ji and W. J. Kim, Stabilization of networked control system with time delays and data-packet losses,, European Journal of Control, 13 (2007), 343.  doi: 10.3166/ejc.13.343-350.  Google Scholar [8] B. Jayawardhana and G. Weiss, Tracking and disturbance rejection for fully actuated mechanical systems,, Automatica, 44 (2008), 2863.  doi: 10.1016/j.automatica.2008.03.030.  Google Scholar [9] S. Liu, L. Xie and H. S. Zhang, Linear quadratic tracking problem for discrete-time systems with multiple delays in single input channel,, International Journal of Robust and Nonlinear Control, 20 (2010), 1379.  doi: 10.1002/rnc.1520.  Google Scholar [10] M. Mauder, Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot,, Automatica, 44 (2008), 2588.  doi: 10.1016/j.automatica.2008.02.012.  Google Scholar [11] A. Naskali and A. Onat, Random network delay in model based predictive networked control systems,, in Proc. $6^{nd}$ WSEAS Int. Conf. Appl. Comput. Sci., 1 (2006), 199.   Google Scholar [12] A. Onat, et al., Control over imperfect networks: Model-based predictive networked control systems,, IEEE Transactions on Industrial Electronics, 58 (2011), 905.  doi: 10.1109/TIE.2010.2051932.  Google Scholar [13] A. Onat and E. Parlakay, Implementation of networked predictive control system,, in Proc. 9th Real-Time Linux Workshop, 1 (2007), 85.   Google Scholar [14] T. Suzuki, et al., Controllability and stabilizability of a networked control system with periodic communication constraints,, Systems & Control Letters, 60 (2011), 977.  doi: 10.1016/j.sysconle.2011.08.004.  Google Scholar [15] Y. Shi and B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains,, IEEE Transactions on Automatic Control, 54 (2009), 1668.  doi: 10.1109/TAC.2009.2020638.  Google Scholar [16] A. Sala, Computer control under time-varying sampling period: An LMI gridding approach,, Automatica, 41 (2005), 2077.  doi: 10.1016/j.automatica.2005.05.017.  Google Scholar [17] B. O. S. Teixeira, et al., Spacecraft tracking using sampled-data Kalman filters - An illustrative application of extended and unscented estimators,, IEEE Control Systems Magazine, 28 (2008), 78.  doi: 10.1109/MCS.2008.923231.  Google Scholar [18] Y. H. Wang, Z. M. Wang and Y. F. Zheng, On the model-based networked control for singularly perturbed systems,, International Journal of Robust and Nonlinear Control, 6 (2008), 153.  doi: 10.1007/s11768-008-6152-9.  Google Scholar [19] J. Wu and T. W. Chen, Design of networked control systems with packet dropouts,, IEEE Transactions on Automatic Control, 52 (2007), 1314.  doi: 10.1109/TAC.2007.900839.  Google Scholar [20] H. H. Wang, Optimal tracking for Discrete-Time Systems with Input Delays,, Proceedings of the 2008 Chinese Control and Decision Conference, (2008), 4033.   Google Scholar [21] Y. L. Wang and G. H. Yang, Output tracking control for networked control systems with time delay and packet dropout,, International Journal of Control, 81 (2008), 1709.  doi: 10.1080/00207170701836944.  Google Scholar [22] Y. Wang and G. Yang, Output tracking control for discrete-time networked control systems,, IEEE American Control Conference, (2009), 5109.  doi: 10.1109/ACC.2009.5159974.  Google Scholar [23] D. Wu, J. Wu and S. Chen, Robust $H_\infty$ control for networked control systems with uncertainties and multiple-packet transmission,, IET Control Theory Appl., 4 (2010), 701.  doi: 10.1049/iet-cta.2009.0090.  Google Scholar [24] Y. L. Wang and G. H. Yang, Output tracking control for continuous-time networked control systems with communication constraints,, Proc. of the American Control Conference, (2009), 531.  doi: 10.1109/ACC.2009.5159975.  Google Scholar [25] H. H. Wang and G. Y. Tang, Observer-based optimal output tracking for discrete-time systems with multiple state and input delays,, International Journal of Control Automation and Systems, 7 (2009), 57.  doi: 10.1007/s12555-009-0108-9.  Google Scholar [26] H. W. Yu, X. M. Zhang, G. P. Lu and Y. F. Zheng, On model based networked control for singularly perturbed systems with nonlinear uncertainties,, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, (2009), 684.  doi: 10.1109/CDC.2009.5400103.  Google Scholar [27] D. Yue, Q. L. Han and J. Lam, Network-based robust $H_\infty$ control of systems with uncertainty,, Automatica, 41 (2005), 999.  doi: 10.1016/j.automatica.2004.12.011.  Google Scholar [28] X. M. Zhang, et al., Stochastic stability of networked control systems with network-induced delay and data dropout,, in Proceedings of the 45th Ieee Conference on Decision and Control, 14 (2006), 5006.  doi: 10.1109/CDC.2006.376970.  Google Scholar [29] H. G. Zhang, J. Yang and C. Y. Su, T-S fuzzy-model-based robust $H_\infty$ design for networked control systems with uncertainties,, IEEE Trans. Ind. Inf., 3 (2007), 289.   Google Scholar [30] Q. Zhang, et al., An Enhanced LMI Approach for Mixed $H_2/H_\infty$ Flight Tracking Control,, Chinese Journal of Aeronautics, 24 (2011), 324.   Google Scholar [31] H. B. Zeng, et al., Absolute stability and stabilization for Lurie networked control systems,, International Journal of Robust and Nonlinear Control, 21 (2011), 1667.  doi: 10.1002/rnc.1658.  Google Scholar
 [1] Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020107 [2] Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019 [3] Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020046 [4] Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444 [5] Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347 [6] Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 243-271. doi: 10.3934/dcdss.2020213 [7] Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020110 [8] Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020032 [9] Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 [10] Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $L^2-$norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 [11] Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chance-constrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial & Management Optimization, 2021, 17 (1) : 67-79. doi: 10.3934/jimo.2019099 [12] M. S. Lee, H. G. Harno, B. S. Goh, K. H. Lim. On the bang-bang control approach via a component-wise line search strategy for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 45-61. doi: 10.3934/naco.2020014 [13] Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011 [14] Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020341 [15] Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial & Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113 [16] Veena Goswami, Gopinath Panda. Optimal customer behavior in observable and unobservable discrete-time queues. Journal of Industrial & Management Optimization, 2021, 17 (1) : 299-316. doi: 10.3934/jimo.2019112 [17] Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020468 [18] Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216 [19] Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323 [20] Zongyuan Li, Weinan Wang. Norm inflation for the Boussinesq system. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020353

2019 Impact Factor: 1.366