Networked predictive control for nonlinear systems with stochastic disturbances in the presence of data losses

Networked control allows monitoring a plant from a remote location through a communication channel and owns several attractive advantages. One of the major challenges is the control problem of stochastic nonlinear systems with packet losses and/or communication delays. In this paper, the networked control of nonlinear systems with stochastic disturbances in the presence of packet losses is investigated. In order to reduce the effect of data packet losses on the system stability, a model predictive control method is proposed to compensate the packet losses in communication channel. By using stochastic stability theory and a previously designed Lyapunov controller, pth moment practical stability of the networked control system (NCS) is discussed, and a sufficient condition guaranteeing the practical stability of the closed-loop system is provided. Based on the sufficient condition, the relation formula between any prior given control target and the corresponding maximum time of consecutive packet losses is derived, and it is found that the ultimate bound of pth moment is mainly dependent on the maximum time of consecutive packet losses. As an example, networked control of the nonlinear chaotic Lorenz system with stochastic disturbances and data packet losses is considered to verify the effectiveness of the proposed method.

[1]  Long Wang,et al.  Stabilization of networked control systems with data packet dropout and network delays via switching system approach , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Panagiotis D. Christofides,et al.  Model-based control of nonlinear systems subject to sensor data losses: A chemical process case study , 2007, 2007 46th IEEE Conference on Decision and Control.

[3]  Zidong Wang,et al.  Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements , 2012, IEEE Transactions on Automatic Control.

[4]  Guo-Ping Liu,et al.  Predictive Controller Design of Networked Systems With Communication Delays and Data Loss , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  J. Doyle,et al.  NONLINEAR OPTIMAL CONTROL: A CONTROL LYAPUNOV FUNCTION AND RECEDING HORIZON PERSPECTIVE , 1999 .

[6]  Gang Feng,et al.  Sampled‐data control of nonlinear networked systems with time‐delay and quantization , 2016 .

[7]  Tamer Basar,et al.  Optimal control of LTI systems over unreliable communication links , 2006, Autom..

[8]  Jianbin Qiu,et al.  Asynchronous Output-Feedback Control of Networked Nonlinear Systems With Multiple Packet Dropouts: T–S Fuzzy Affine Model-Based Approach , 2011, IEEE Transactions on Fuzzy Systems.

[9]  Senchun Chai,et al.  Design, Simulation and Implementation of Networked Predictive Control Systems , 2005 .

[10]  Xianzhong Chen,et al.  Iterative Distributed Model Predictive Control of Nonlinear Systems: Handling Asynchronous, Delayed Measurements , 2012, IEEE Transactions on Automatic Control.

[11]  Tai C Yang,et al.  Networked control system: a brief survey , 2006 .

[12]  Jianbin Qiu,et al.  Nonsynchronized Robust Filtering Design for Continuous-Time T–S Fuzzy Affine Dynamic Systems Based on Piecewise Lyapunov Functions , 2013, IEEE Transactions on Cybernetics.

[13]  Panagiotis D. Christofides,et al.  Lyapunov-based Model Predictive Control of Nonlinear Systems Subject to Data Losses , 2007, ACC.

[14]  Hao Zhang,et al.  Quantized Control Design for Impulsive Fuzzy Networked Systems , 2011, IEEE Transactions on Fuzzy Systems.

[15]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[16]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[17]  Guo-Ping Liu,et al.  A Predictive Control-Based Approach to Networked Hammerstein Systems: Design and Stability Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Panagiotis D. Christofides,et al.  Multirate distributed model predictive control of nonlinear systems , 2011, Proceedings of the 2011 American Control Conference.

[19]  Hong Ye,et al.  Scheduling of networked control systems , 2001 .

[20]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[21]  Jun Hu,et al.  Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements , 2013, Int. J. Control.

[22]  Guo-Ping Liu,et al.  Predictive Output Feedback Control for Networked Control Systems , 2014, IEEE Transactions on Industrial Electronics.

[23]  Guo-Ping Liu,et al.  NETWORKED PREDICTIVE CONTROL OF SYSTEMS WITH RANDOM COMMUNICATION DELAY , 2004 .

[24]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[25]  Jun Hu,et al.  State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays , 2014, Int. J. Gen. Syst..

[26]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[27]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[28]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[29]  Thomas Parisini,et al.  Networked Predictive Control of Uncertain Constrained Nonlinear Systems: Recursive Feasibility and Input-to-State Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[30]  Juan C. Vasquez,et al.  Robust Networked Control Scheme for Distributed Secondary Control of Islanded Microgrids , 2014, IEEE Transactions on Industrial Electronics.

[31]  Hamid Reza Karimi,et al.  New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions , 2015, J. Frankl. Inst..

[32]  Yeng Chai Soh,et al.  LQG Control for Networked Control Systems with Random Packet Delays and Dropouts via Multiple Predictive-Input Control Packets , 2011 .

[33]  Xiao Jian,et al.  Communication and control co-design for networked control system in optimal control , 2008, ICONS 2008.

[34]  Soura Dasgupta,et al.  NONLINEAR OPTIMAL CONTROL , 2007 .

[35]  Hongyi Li,et al.  Tracking control for polynomial fuzzy networked systems with repeated scalar nonlinearities , 2016, Neurocomputing.

[36]  Derong Liu,et al.  Networked Control Systems: Theory and Applications , 2008 .

[37]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[38]  Xuerong Mao,et al.  On Input-to-State Stability of Stochastic Retarded Systems With Markovian Switching , 2009, IEEE Transactions on Automatic Control.