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IEEE/CAA Journal of Automatica Sinica

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M. Fu, “A tutorial on quantized feedback control,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 5–17, Jan. 2024. doi: 10.1109/JAS.2023.123972
Citation: M. Fu, “A tutorial on quantized feedback control,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 5–17, Jan. 2024. doi: 10.1109/JAS.2023.123972

A Tutorial on Quantized Feedback Control

doi: 10.1109/JAS.2023.123972
Funds:  This work was partially supported by National Natural Science Foundation of China (62350710214, U23A20325) and Shenzhen Key Laboratory of Control Theory and Intelligent Systems (ZDSYS20220330161800001)
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  • In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of feedback information, such as measurements and control signals, over digital networks, presenting novel challenges in estimation and control design. Our examination encompasses various topics, including the minimal information needed for effective feedback control, the design of quantizers, strategies for quantized control design and estimation, achieving consensus control with quantized data, and the pursuit of high-precision tracking using quantized measurements.

     

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  • 1 A system is said to be quadratically stable if its stability can be asserted by using a quadratic Lyapunov function.
  • [1]
    J. B. Lewis and J. T. Tou, “Optimum sampled-data systems with quantized control signals,” Trans. AIEE, vol. 82, no. 2, pp. 195–201, Jul. 1965.
    [2]
    L. Meier, “Combined optimal control and estimation,” in Proc. Allerton Conf. Circuit and System Theory, pp. 109–120, 1965.
    [3]
    J. T. Tou, Optimum Design of Digital Control Systems, New York: Academic, 1963.
    [4]
    R. E. Larson, “Optimum quantization in dynamic systems,” IEEE Trans. Automatic Control, vol. AC-12, no. 2, pp. 162–168, 1967.
    [5]
    T. R. Fischer, “Optimal quantized control,” IEEE Trans. Autom. Control, vol. AC-27, no. 4, pp. 996–998, 1982.
    [6]
    R. E. Kalman, “Nonlinear aspects of sampled-data control systems,” in Proc. Symp. Nonlinear Circuit Theory, vol. VII. Brooklyn, NY: Polytechnic Press, 1956.
    [7]
    B. Widrow, “Statistical analysis of amplitude-quantized sampled-data systems,” Trans. AIEE, vol. 79, no. 2, pp. 555–567, January. 1961.
    [8]
    D. F. Delchamps, “Stabilizing a linear system with qunatized state feedback,” IEEE Trans. Automatic Control, vol. 35, no. 8, pp. 916–924, 1990. doi: 10.1109/9.58500
    [9]
    W. S. Wong and R. W. Brockett, “Systems with finite communication bandwidth constraints I: State estimation problems,” IEEE Trans. Automatic Control, vol. 42, no. 9, pp. 1294–1299, 1997. doi: 10.1109/9.623096
    [10]
    W. S. Wong and R. W. Brockett, “Systems with finite communication bandwidth constraints II: Stabilization with limited information feedback,” IEEE Trans. Automatic Control, vol. 44, no. 5, pp. 1049–1053, 1999. doi: 10.1109/9.763226
    [11]
    J. Baillieul, “Feedback designs in information-based control,” in Stochastic Theory and Control Workshop, Kansis, Springer, pp. 35–57, 2001.
    [12]
    V. Borkar and S. Mitter, “LQG control with communication constraints,” in Communications, Computation, Control and Signal Processing: A Tribute to Thomas Kailath. Norwell, MA: Kluwer, 1997.
    [13]
    R. W. Brockett and D. Liberzon, “Quantized feedback stabilization of linear systems,” IEEE Trans. Automatic Control, vol. 45, no. 7, pp. 1279–1289, 2000. doi: 10.1109/9.867021
    [14]
    G. N. Nair and R. J. Evans, “Stabilization with data-rate-limited feedback: Tightest attainable bounds,” Systems and Control Letters, vol. 41, pp. 49–56, 2000. doi: 10.1016/S0167-6911(00)00037-2
    [15]
    G. N. Nair and R. J. Evans, “Exponential stabilisability of finite-dimensional linear systems with limited data rates,” Automatica, vol. 39, pp. 585–593, 2003. doi: 10.1016/S0005-1098(02)00285-6
    [16]
    N. Elia and K. Mitter, “Stabilization of linear systems with limited information,” IEEE Trans. Automatic Control, vol. 46, no. 9, pp. 1384–1400, 2001. doi: 10.1109/9.948466
    [17]
    S. Tatikonda and S. Mitter, “Control under communication constraints,” IEEE Trans. Automatic Control, vol. 49, no. 7, pp. 1056–1068, 2004. doi: 10.1109/TAC.2004.831187
    [18]
    S. Tatikonda and S. Mitter, “Control over noisy channels,” IEEE Trans. Automatic Control, vol. 49, no. 7, pp. 1196–1201, 2004. doi: 10.1109/TAC.2004.831102
    [19]
    M. Fu and L. Xie, “The sector bound approach to quantized feedback control,” IEEE Trans. Automatic Control, vol. 50, no. 11, pp. 1698–1711, Nov. 2005. doi: 10.1109/TAC.2005.858689
    [20]
    M. Fu and L. Xie, “Finite-level quantization feedback control for linear systems,” IEEE Trans. Automatic Control, vol. 54, no. 5, pp. 1165–1170, May 2009. doi: 10.1109/TAC.2009.2017815
    [21]
    N. Xiao, L. Xie, and M. Fu, “Stabilization of Markov jump linear systems using quantized state feedback,” Automatica, vol. 46, no. 10, pp. 1696–1702, 2010. doi: 10.1016/j.automatica.2010.06.018
    [22]
    D. Coutinho, M. Fu, and C. E. de Souza, “Input and output quantized feedback linear systems,” IEEE Trans. Automatic Control, vol. 55, no. 3, pp. 761–766, 2010. doi: 10.1109/TAC.2010.2040497
    [23]
    D. Liberzon, “On stabilization of linear systems with limited information,” IEEE Trans. Automatic Control, vol. 48, pp. 304–307, 2003. doi: 10.1109/TAC.2002.808487
    [24]
    S. Taikonda, A. Sahai, and S. Mitter, “Stochastic linear control over a communication channel,” IEEE Trans. Automatic Control, vol. 49, no. 9, pp. 1549–1561, 2004. doi: 10.1109/TAC.2004.834430
    [25]
    A. S. Matveev and A. V. Savkin, “The problem of LQG optimal control via a limited capacity communication channel,” Systems and Control Letters, vol. 53, pp. 51–64, 2004. doi: 10.1016/j.sysconle.2004.02.021
    [26]
    M. Fu, “Lack of separation principle for quantized linear quadratic Gaussian control,” IEEE Trans. Automatic Control, vol. 57, no. 9, pp. 2385–2390, 2012. doi: 10.1109/TAC.2012.2187010
    [27]
    M. Fu, “Linear quadratic Gaussian control with quantized feedback,” in Proc. American Control Conf., St. Louis, July 2009.
    [28]
    M. Fu and C. E. de Souza, “State estimation for linear discrete-time systems using quantized measurements,” Automatica, vol. 45, no. 12, pp. 2937–2945, 2009. doi: 10.1016/j.automatica.2009.09.033
    [29]
    M. Epstein, L. Shi, A. Tiwari, and R. Murry, “Probabilistic performance of state estimation across a lossy network,” Automatica, vol. 44, no. 12, pp. 3046–3053, 2008. doi: 10.1016/j.automatica.2008.05.026
    [30]
    A. Tiwari, M. Jun, D. Jeffcoat, and R. Murray, “Analysis of dynamic sensor coverage problem using Kalman filters for estimation,” in Proc. 16th IFAC World Congr., Prague, Czech Republic, 2005.
    [31]
    R. Carli, F. Fagnani, P. Frasca, and S. Zampieri, “Efficient quantized techniques for consensus algorithms,” in Proc. NeCST Workshop, Nancy, France, 2001.
    [32]
    R. Carli, F. Fagnani, P. Frasca, and S. Zampieri, “A probabilistic analysis of the average consensus algorithm with quantized communication,” in Proc. 17th IFAC World Congr., Seoul, Korea, 2008.
    [33]
    N. Xiao, L. Xie, and M. Fu, “Kalman filtering over unreliable communication networks with bounded Markovian packet dropouts,” Int. J. Robust and Nonlinear Control, vol. 19, no. 16, pp. 1770–1786, 2009. doi: 10.1002/rnc.1389
    [34]
    M. Fu, “Distributed consensus with limited communication data rate,” IEEE Trans. Automatic Control, vol. 56, no. 2, pp. 279–292, 2011. doi: 10.1109/TAC.2010.2052384
    [35]
    W. Chen, Z. Wang, D. Ding, and H. Dong, “Consensusability of discrete-time multi-agent systems under binary encoding with bit errors,” Automatica, vol. 133, p. 109867, 2021. doi: 10.1016/j.automatica.2021.109867
    [36]
    A. Salton, J. V. Flores, J. Zheng, and M. Fu, “Asymptotic tracking of discrete-time systems subject to uniform output quantization,” IEEE Control Systems Letters, vol. 7, no. 2, pp. 829–834, 2023.
    [37]
    A. T. Salton, M. Fu, J. V. Flores, and J. Zheng, “High precision over long range: A macro-micro approach to quantized positioning systems,” IEEE Trans. Control Systems Technology, vol. 29, no. 6, pp. 2406–2415, 2021. doi: 10.1109/TCST.2020.3041172
    [38]
    A. T. Salton, J. Zheng, J. V. Flores, and M. Fu, “High-precision tracking of periodic signals: A macro-micro approach with quantized feedback,” IEEE Trans. Industrial Electronics, vol. 69, no. 8, pp. 8325–8334, 2022. doi: 10.1109/TIE.2021.3109511
    [39]
    F. C. Rego et al., “A distributed Luenberger observer for linear state feedback systems with quantized and rate-limited communications,” IEEE Trans. Automatic Control, vol. 66, no. 9, pp. 3922–3937, 2021. doi: 10.1109/TAC.2020.3027658
    [40]
    Y. H. Choi and S. J. Yoo, “Distributed quantized feedback design strategy for adaptive consensus tracking of uncertain strict-feedback nonlinear multiagent systems with state quantizers,” IEEE Trans. Cybernetics, vol. 52, no. 7, pp. 7069–7083, 2022. doi: 10.1109/TCYB.2021.3049488
    [41]
    Z. Zhang, J. Hu, and H. Huang, “Formation tracking for nonlinear uncertain multi-agent systems via adaptive output feedback quantized control,” IEEE Access, vol. 7, 2019. doi: 10.1109/ACCESS.2019.2929267
    [42]
    L. Zhang, C. Hua, H. Yu, and X. Guan, “Distributed adaptive fuzzy containment control of stochastic pure-feedback nonlinear multiagent systems with local quantized controller and tracking constraint,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 49, no. 4, pp. 787–796, 2019. doi: 10.1109/TSMC.2017.2701344
    [43]
    Z. Zhang, C. Wen, L. Xing, and Y. Song, “Adaptive output feedback control of nonlinear systems with mismatched uncertainties under input/output quantization,” IEEE Trans. Automatic Control, vol. 67, no. 9, pp. 4801–4808, 2022. doi: 10.1109/TAC.2022.3159543
    [44]
    X. Xia, T. Zhang, Y. Fang, and G. Kang, “Adaptive quantized control of output feedback nonlinear systems with input unmodeled dynamics based on backstepping and small-gain method,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 9, pp. 5686–5697, 2021. doi: 10.1109/TSMC.2019.2956997
    [45]
    X. Yu and Y. Lin, “Adaptive backstepping quantized control for a class of nonlinear systems,” IEEE Trans. Automatic Control, vol. 62, no. 2, pp. 981–985, 2017. doi: 10.1109/TAC.2016.2570140
    [46]
    S. Dey, A. Chiuso, and L. Schenato, “Feedback control over lossy SNR-limited channels: Linear encoder-decoder-controller design,” IEEE Trans. Automatic Control, vol. 62, no. 6, pp. 3054–3061, 2017. doi: 10.1109/TAC.2017.2674024
    [47]
    M. Zhang, P. Shi, L. Ma, J. Cai, and H. Su, “Quantized feedback control of fuzzy Markov jump systems,” IEEE Trans. Cybernetics, vol. 49, no. 9, pp. 3375–3384, 2019. doi: 10.1109/TCYB.2018.2842434
    [48]
    M. Xu, Z. Xu, L. Ma, and H. Que, “Quantized H feedback control of semi-Markov jump systems with limited mode information,” IEEE Access, vol. 8, 2020. doi: 10.1109/ACCESS.2020.2997786
    [49]
    A. V. Papadopoulos, F. Terraneo, A. Leva, and M. Prandini, “Switched control for quantized feedback systems: Invariance and limit cycle analysis,” IEEE Trans. Automatic Control, vol. 63, no. 11, pp. 3775–3786, 2018. doi: 10.1109/TAC.2018.2797246
    [50]
    M. Wakaiki, T. Zanma, and K.-Z. Liu, “Observer-based stabilization of systems with quantized inputs and outputs,” IEEE Trans. Automatic Control, vol. 64, no. 7, pp. 2929–2936, 2019. doi: 10.1109/TAC.2018.2873355
    [51]
    J. Wang, “Quantized feedback control based on spherical polar coordinate quantizer,” IEEE Trans. Automatic Control, vol. 66, no. 12, pp. 6077–6084, 2021. doi: 10.1109/TAC.2021.3059845
    [52]
    W. Liu, Q. Ma, S. Xu, and Z. Zhang, “State quantized output feedback control for nonlinear systems via event-triggered sampling,” IEEE Trans. Automatic Control, vol. 67, no. 12, pp. 6810–6817, 2022. doi: 10.1109/TAC.2021.3135390
    [53]
    J. Lian and C. Li, “Event-triggered sliding mode control of uncertain switched systems via hybrid quantized feedback,” IEEE Trans. Automatic Control, vol. 66, no. 6, pp. 2809–2816, 2021. doi: 10.1109/TAC.2020.3009199
    [54]
    M. Abdelrahim, V. S. Dolk, and W. P. M. H. Heemels, “Event-triggered quantized control for input-to-state stabilization of linear systems with distributed output sensors,” IEEE Trans. Automatic Control, vol. 64, no. 12, pp. 4952–4967, 2019. doi: 10.1109/TAC.2019.2900338
    [55]
    M. Ran, S. Feng, J. Li, and L. Xie, “Quantized consensus under data-rate constraints and DoS attacks: A zooming-in and holding approach,” IEEE Trans. Automatic Control, vol. 68, no. 9, pp. 5397–5412, 2023. doi: 10.1109/TAC.2022.3223277
    [56]
    L.-Y. Hao, Y. Yu, T.-S. Li, and H. Li, “Quantized output-feedback control for unmanned marine vehicles with thruster faults via sliding-mode technique,” IEEE Trans. Cybernetics, vol. 52, no. 9, pp. 9363–9376, 2022. doi: 10.1109/TCYB.2021.3050003
    [57]
    J. Liu and N. Elia, “Quantized control with applications to mobile vehicles,” in Proc. IEEE Conf. Decision and Control, 2002.
    [58]
    S. M. M. Uddin and G. Mirzaeva, “A high performance feedback quantized predictive control of induction machine drives,” in Proc. IEEE Energy Conversion Congr. and Exposition, 2020.
    [59]
    C. Zhang, Y. Yu, and M. Zhou, “Finite-time adaptive quantized motion control for hysteretic systems with application to piezoelectric-driven micropositioning stage,” IEEE/ASME Trans. Mechatronics, 2023. DOI: 10.1109/TMECH.2023.3250481
    [60]
    A. Sahai, “The necessity and sufficiency of anytime capacity for control over a noisy communication link,” in Proc. IEEE Conf. Decision and Control, 2004.
    [61]
    A. Rao, D. Miller, K. Rose, and A. Gersho, “Generalized vector quantization: Jointly optimal quantization and estimation,” in Proc. IEEE Int. Symp. Information Theory, 1995.
    [62]
    L. Xiao and S. Boyd, “Fast linear iterations for distributed averaging,” Systems and Control Letters, vol. 53, pp. 65–78, 2004. doi: 10.1016/j.sysconle.2004.02.022
    [63]
    R. Olfati-Saber and R. M. Murray, “Consensus problem in networks of agents with switching topology and time-delays,” IEEE Trans. Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004. doi: 10.1109/TAC.2004.834113
    [64]
    Y. Xu, Z. Wu, Y. Pan, C. K. Ahn, and H. Yan, “Consensus of linear multiagent systems with input-based triggering condition,” IEEE Trans. Systems,Man and Cybernetics: Systems, vol. 49, no. 11, pp. 2308–2317, 2018.
    [65]
    Y. Chen and Y. Shi, “Distributed consensus of linear multiagent systems: Laplacian spectra-based method,” IEEE Trans. Systems,Man and Cybernetics: Systems, vol. 50, no. 2, pp. 700–706, 2020. doi: 10.1109/TSMC.2017.2774841
    [66]
    J. Zhou, Y. Zhu, Z. You, and E. Song, “An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems,” IEEE Trans. Systems,Man and Cybernetics-Part A: Systems and Humans, vol. 36, no. 5, pp. 1000–1009, 2006. doi: 10.1109/TSMCA.2006.878986
    [67]
    S. Yang, Q. Liu, and J. Wang, “Distributed optimization based on a multiagent system in the presence of communication delays,” IEEE Trans. Systems,Man and Cybernetics: Systems, vol. 47, no. 5, pp. 717–728, 2016.
    [68]
    K. Xie, Q. Cai, Z. Zhang, and M. Fu, “Distributed algorithms for average consensus of input data with fast convergence,” IEEE Trans. Systems,Man and Cybernetics: Systems, vol. 51, no. 5, pp. 2653–2664, 2021. doi: 10.1109/TSMC.2019.2914385
    [69]
    L. Hitz and B. D. O. Anderson, “Discrete positive-real functions and their application to system stability,” Proc. IEE, vol. 116, no. 1, pp. 153–155, 1969.

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    Highlights

    • This tutorial paper delves into quantized feedback control, tackling the challenges associated with transmitting feedback information, including measurements and control signals, over digital networks. Additionally, it explores strategies to mitigate the impact of quantization errors
    • Examined topics include minimal information for effective control, quantizer design, strategies for quantized control and estimation, achieving consensus control with quantized data, and high-precision tracking using quantized measurements
    • Provided insights into techniques addressing diverse quantized feedback problems, such as connecting logarithmic quantization to robust control under sector-bounded uncertainties, practical implementation of dynamic scaling for quantization, analysis of the absence of a separation principle for quantized LQG control, exploration of the tradeoff between average consensus precision and convergence rate, and strategies for mitigating quantization error in periodic signal tracking control

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