Optimal tracking performance of discrete-time systems with quantization

Volume 10, Issue 4, pp 1873--1880 http://dx.doi.org/10.22436/jnsa.010.04.47

Publication Date: April 20, 2017 Submission Date: July 11, 2016

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Authors

Chao-Yang Chen - School of Information Science and Engineering, Central South University, Changsha, 410012, P. R. China. - School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, P. R. China. Weihua Gui - School of Information Science and Engineering, Central South University, Changsha, 410012, P. R. China. Shaowu Zhou - School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, P. R. China. Zhi-Wei Liu - College of Automation, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China. Zhi-Hong Guan - College of Automation, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China. Ning Gui - School of Information, Zhejiang Sci-Tech University, Hangzhou, 310018, P. R. China.

Abstract

This paper studies optimal tracking performance issues for linear time invariant system with two-channel constraints. The specific problem under consideration is quantization for up-link and down-link communication channel which satisfies some constraints. Logarithmic quantization law is employed in the quantizers. The tracking performance is defined in an square sense, and the reference signal under consideration in this paper is a step signal. The system’s reference signal is considered as a step signal. The tracking performance is measured by the minimum mean square error between the reference input and the system’s output. By using dynamic programming approach, discrete-time algebraic Riccati equation (ARE) is obtained. The optimal tracking performance is obtained by output feedback control, in terms of the space equation of the given system and the unique solution of the discrete-time algebraic Riccati equation. And, the impact of quantizer for optimal tracking performance is analyzed. Finally, simulation example is given to illustrate the theoretical results.

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Keywords

• Optimal tracking performance
• quantization
• two-channel constraints
• discrete-time systems
• algebraic Riccati equation (ARE).

MSC

•  29J21

References

• [1] M. Ait Rami, X. Chen, X. Y. Zhou, Discrete-time indefinite LQ control with state and control dependent noises, Nonconvex optimization in control, J. Global Optim., 23 (2002), 245–265.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] C.-Y. Chen, Z.-H. Guan, M. Chi, Y.-H. Wu, X.-W. Jiang, Fundamental performance limitations of networked control systems with novel trade-off factors and constraint channels, J. Franklin Inst., 354 (2017), 3120–3133.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] C.-Y. Chen, B. Hu, Z.-H. Guan, M. Chi, D.-X. He, Optimal tracking performance of control systems with two-channel constraints, Inf. Sci., 374 (2016), 85–99.
  • View Article
  • Google Scholar


• [4] X.-M. Chen, Z.-Y. Zhang, S.-L. Chen, Finite-signal-to-noise ratio diversity-multiplexing-rate trade-off in limited feedback beamforming systems with imperfect channel state information, IET Commun., 6 (2012), 751–758.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] X. Cong, K. Shuang, S. Su, F.-C. Yang, An efficient server bandwidth costs decreased mechanism towards mobile devices in cloud-assisted P2P-VoD system, Peer-to-Peer Netw. Appl., 7 (2014), 175–187.
  • View Article
  • Google Scholar


• [6] J.-W. Dong, W.-J. Kim, Bandwidth allocation and scheduling of networked control systems with exponential and quadratic approximations, Control Eng. Pract., 26 (2014), 72–81.
  • View Article
  • Google Scholar


• [7] H. Fares, C. Langlais, Finite-signal-to-noise ratio diversity-multiplexing-delay tradeoff in half-duplex hybrid automatic repeat request relay channels, IET Commun., 9 (2015), 872–879.
  • View Article
  • Google Scholar


• [8] M.-Y. Fu, L.-H. Xie, The sector bound approach to quantized feedback control, IEEE Trans. Automat. Control, 50 (2005), 1698–1711.
  • View Article
  • MathSciNet
  • Google Scholar


• [9] E. Garcia, P. J. Antsaklis, Model-based event-triggered control for systems with quantization and time-varying network delays, IEEE Trans. Automat. Control, 58 (2013), 422–434.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] M.-F. Ge, Z.-H. Guan, C. Yang, C.-Y. Chen, D.-F. Zheng, M. Chi, Task-space coordinated tracking of multiple heterogeneous manipulators via controller-estimator approaches, J. Franklin Inst., 353 (2016), 3722–3738.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] Z.-H. Guan, C.-Y. Chen, G. Feng, T. Li, Optimal tracking performance limitation of networked control systems with limited bandwidth and additive colored white Gaussian noise, IEEE Trans. Circuits Syst. I, Reg. Papers, 60 (2013), 189–198.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] Y.-Q. Li, J. Chen, E. Tuncel, W.-Z. Su, MIMO control over additive white noise channels: stabilization and tracking by LTI controllers, IEEE Trans. Automat. Control, 61 (2016), 1281–1296.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] F.-W. Li, X.-C. Wang, P. Shi, Robust quantized \(H_\infty\) control for network control systems with Markovian jumps and time delays, Int. J. Innov. Comput. I., 9 (2013), 4889–4902.
  • Google Scholar


• [14] F. Mazenc, M. Malisoff, Trajectory based approach for the stability analysis of nonlinear systems with time delays, IEEE Trans. Automat. Control, 60 (2015), 1716–1721.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] C. Peng, T. C. Yang, Event-triggered communication and \(H_\infty\) control co-design for networked control systems, Automatica J. IFAC, 49 (2013), 1326–1332.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] T. Qi, W.-Z. Su, J. Chen, Tracking performance for output feedback control under quantization constraints, Proc. 30th Chinese Control Conf., Yantai, (2011), 6419–6424.
  • Google Scholar


• [17] A. J. Rojas, Signal-to-noise ratio fundamental limitations in the discrete-time domain, Systems Control Lett., 61 (2012), 55–61.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] E. I. Silva, G. C. Goodwin, D. E. Quevedo, Control system design subject to SNR constraints, Automatica J. IFAC, 46 (2010), 428–436.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] L.-K. Sun, J.-G. Wu, Schedule and control co-design for networked control systems with bandwidth constraints, J. Franklin Inst., 351 (2014), 1042–1056.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] B.-X. Wang, X.-W. Jiang, C.-Y. Chen, Trade-off performance analysis of LTI system with channel energy constraint, ISA Trans., 65 (2016), 88–95.
  • View Article
  • Google Scholar


• [21] Y.-W. Wang, W. Yang, J.-W. Xiao, Z.-G. Zeng, Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., PP, (2016), 1560 - 1571
  • View Article
  • MathSciNet
  • Google Scholar


• [22] L. Wei, M.-Y. Fu, H.-S. Zhang, Quantized output feedback control with multiplicative measurement noises, Internat. J. Robust Nonlinear Control, 25 (2015), 1338–1351.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] X.-S. Zhan, J. Wu, T. Jiang, X.-W. Jiang, Optimal performance of networked control systems under the packet dropouts and channel noise, ISA Trans., 58 (2015), 214–221.
  • View Article
  • Google Scholar


• [24] L.-X. Zhang, H.-J. Gao, O. Kaynak, Network-induced constraints in networked control systems–a survey, IEEE Trans. Ind. Informat., 9 (2016), 403–416.
  • View Article
  • Google Scholar


• [25] H. Zhang, Y. Shi, A. S. Mehr, Robust \(H_\infty\) PID control for multivariable networked control systems with disturbance/noise attenuation, Internat. J. Robust Nonlinear Control, 22 (2012), 183–204.
  • View Article
  • Google Scholar
  • MATH


• [26] X.-S. Zhao, Z.-H. Guan, F.-S. Yuan, X.-H. Zhang, Optimal performance of discrete-time control systems based on networkinduced delay, Eur. J. Control, 19 (2013), 37–41.
  • View Article
  • MathSciNet
  • Google Scholar


• [27] X.-W. Zhao, B. Hu, Z.-H. Guan, C.-Y. Chen, M. Chi, X.-H. Zhang, Multi-flocking of networked non-holonomic mobile robots with proximity graphs, IET Control Theory Appl., 10 (2016), 2093–2099.
  • View Article
  • MathSciNet
  • Google Scholar


• [28] Q. Zhou, P. Shi, S.-Y. Xu, H.-Y. Li, Observer-based adaptive neural network control for nonlinear stochastic systems with time delay, IEEE Trans. Neural Netw. Learn. Syst., 24 (2013), 71–80.
  • View Article
  • Google Scholar