A Review on Analysis and Synthesis of Nonlinear Stochastic Systems with Randomly Occurring Incomplete Information

In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.

[1]  Zheng Yufan,et al.  Nonlinear H ∞ filtering for interconnected Markovian jump systems , 2006 .

[2]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[3]  J. Lam,et al.  Fixed-Order Robust Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities , 2006 .

[4]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[5]  James Lam,et al.  Non-Fragile Exponential Stability Assignment of Discrete-Time Linear Systems With Missing Data in Actuators , 2009, IEEE Transactions on Automatic Control.

[6]  João Yoshiyuki Ishihara,et al.  Information filtering and array algorithms for discrete-time Markovian jump linear systems , 2007, 2007 American Control Conference.

[7]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[8]  Bor-Sen Chen,et al.  Robust Filtering for Nonlinear , 2005 .

[9]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[10]  V A Ugrinovskii,et al.  Distributed robust filtering with H∞ consensus of estimates , 2010, Proceedings of the 2010 American Control Conference.

[11]  Ali H. Sayed,et al.  Diffusion Strategies for Distributed Kalman Filtering and Smoothing , 2010, IEEE Transactions on Automatic Control.

[12]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[13]  Donghua Zhou,et al.  Robust fault detection for networked systems with communication delay and data missing , 2009, Autom..

[14]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[15]  Minyue Fu,et al.  State estimation for linear discrete-time systems using quantized measurements , 2009, Autom..

[16]  Huajing Fang,et al.  Takagi-sugeno fuzzy-model-based fault detection for networked control systems with Markov delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Nan Xiao,et al.  Stabilization of Markov jump linear systems using quantized state feedback , 2010, Autom..

[18]  Ali H. Sayed,et al.  Diffusion strategies for distributed Kalman filtering: formulation and performance analysis , 2008 .

[19]  E. Boukas,et al.  New approach to H ∞ control for Markovian jump singular systems , 2010 .

[20]  Maryam Kamgarpour,et al.  Convergence properties of a decentralized Kalman filter , 2008, 2008 47th IEEE Conference on Decision and Control.

[21]  Torsten Jeinsch,et al.  A unified approach to the optimization of fault detection systems , 2000 .

[22]  Ruzena Bajcsy,et al.  Distributed control of systems over communication networks , 2000 .

[23]  Huijun Gao,et al.  Observer‐based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses , 2010 .

[24]  Yugang Niu,et al.  Stabilization of Markovian jump linear system over networks with random communication delay , 2009, Autom..

[25]  Edwin Engin Yaz,et al.  Robust minimum variance linear state estimators for multiple sensors with different failure rates , 2007, Autom..

[26]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[27]  Peng Jiang,et al.  Distributed state estimation based on quantized observations in a bandwidth constrained sensor network , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[28]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

[29]  Zongli Lin,et al.  Robust filtering for discrete-time systems with saturation and its application to transmultiplexers , 2004, IEEE Transactions on Signal Processing.

[30]  Liang Lu,et al.  Analysis and design of singular linear systems under actuator saturation and L2/linfintyA disturbances , 2008, Syst. Control. Lett..

[31]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[32]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[33]  James Lam,et al.  Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities , 2006, IEEE Transactions on Signal Processing.

[34]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[35]  A. Hermoso-Carazo,et al.  Signal estimation with nonlinear uncertain observations using covariance information , 2009 .

[36]  Zidong Wang,et al.  A delay-dependent approach to H ∞ filtering for stochastic delayed jumping systems with sensor non-linearities , 2007, Int. J. Control.

[37]  Zongli Lin,et al.  An output feedback /spl Hscr//sub /spl infin// controller design for linear systems subject to sensor nonlinearities , 2003 .

[38]  K.H. Johansson,et al.  Quantized agreement under time-varying communication topology , 2008, 2008 American Control Conference.

[39]  James Lam,et al.  Fuzzy-Model-Based Robust Fault Detection With Stochastic Mixed Time Delays and Successive Packet Dropouts , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Daniel W. C. Ho,et al.  A note on the robust stability of uncertain stochastic fuzzy systems with time-delays , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[41]  Fuchun Sun,et al.  Design of reduced-order H∞ filter for Markovian jumping systems with time delay , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[42]  Sirish L. Shah,et al.  Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations , 2007, Int. J. Control.

[43]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.

[44]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[45]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[46]  Huijun Gao,et al.  H∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links , 2009, Signal Process..

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

[48]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2002, IEEE Trans. Autom. Control..

[49]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and I-disturbances , 2004, Autom..

[50]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[51]  Fuwen Yang,et al.  Robust $H_{\infty}$ Control for Networked Systems With Random Packet Losses , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[52]  Sophie Tarbouriech,et al.  Dynamic output controller design for linear systems with actuator and sensor saturation , 2007, 2007 American Control Conference.

[53]  Jun Yang,et al.  Fuzzy Model-Based Robust Networked Control for a Class of Nonlinear Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[54]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[55]  T. Başar,et al.  ℒ1 adaptive controller for quantized systems , 2011, Proceedings of the 2011 American Control Conference.

[56]  Chi-Yi Tsai,et al.  Visual Tracking Control of a Wheeled Mobile Robot With System Model and Velocity Quantization Robustness , 2009, IEEE Transactions on Control Systems Technology.

[57]  Guang-Ren Duan,et al.  H∞ filtering for multiple-time-delay measurements , 2006, IEEE Trans. Signal Process..

[58]  Marcello Farina,et al.  Distributed moving horizon estimation for sensor networks* *The research of M. Farina and R. Scattolini has been supported by the European 7th framework STREP project “Hierarchical and distributed model predictive control (HD-MPC)”, contract number INFSO-ICT-223854. , 2009 .

[59]  Jinzhi Wang,et al.  Output feedback H controller design for linear discrete-time systems with sensor nonlinearities , 2005 .

[60]  Takayuki Nakamura,et al.  Development of self-learning vision-based mobile robots for acquiring soccer robots behaviors , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[61]  Bor-Sen Chen,et al.  Robust H∞ filtering for nonlinear stochastic systems , 2005 .

[62]  Lihua Xie,et al.  Optimal linear estimation for systems with multiple packet dropouts , 2008, Autom..

[63]  Huijun Gao,et al.  Distributed Filtering for a Class of Time-Varying Systems Over Sensor Networks With Quantization Errors and Successive Packet Dropouts , 2012, IEEE Transactions on Signal Processing.

[64]  Huijun Gao,et al.  Fault Detection for Markovian Jump Systems With Sensor Saturations and Randomly Varying Nonlinearities , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[65]  Huijun Gao,et al.  ${H}_{\infty }$ Filtering for Discrete-Time State-Delayed Systems With Finite Frequency Specifications , 2011, IEEE Transactions on Automatic Control.

[66]  Daniel W. C. Ho,et al.  Robust $H_{\infty }$ Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements , 2010, IEEE Transactions on Fuzzy Systems.

[67]  Guoliang Wei,et al.  H∞ filtering for uncertain time‐varying systems with multiple randomly occurred nonlinearities and successive packet dropouts , 2011 .

[68]  Ming Liu.  Network-based stability analysis and synthesis for stochastic system with Markovian switching , 2009 .

[69]  Ruggero Carli,et al.  Distributed Kalman filtering based on consensus strategies , 2008, IEEE Journal on Selected Areas in Communications.

[70]  Daniel W. C. Ho,et al.  Filtering on nonlinear time-delay stochastic systems , 2003, Autom..

[71]  Huijun Gao,et al.  Robust H∞ filtering of nonlinear networked systems with multiple stochastic communication delays , 2009, 2009 7th Asian Control Conference.

[72]  Huijun Gao,et al.  Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks With Defective Statistics of Modes Transitions , 2011, IEEE Transactions on Neural Networks.

[73]  Li Ma,et al.  Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[74]  Reza Olfati-Saber,et al.  Kalman-Consensus Filter : Optimality, stability, and performance , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[75]  Qing-Long Han,et al.  On Designing Fuzzy Controllers for a Class of Nonlinear Networked Control Systems , 2008, IEEE Transactions on Fuzzy Systems.

[76]  Zidong Wang,et al.  H∞ filtering with randomly occurring sensor saturations and missing measurements , 2012, Autom..

[77]  Huijun Gao,et al.  A new approach to quantized feedback control systems , 2008, Autom..

[78]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[79]  Zidong Wang,et al.  Variance-Constrained Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements : The Finite-Horizon Case , 2010 .

[80]  L. Wei,et al.  Near-optimum serial concatenation of single-parity codes with convolutional codes , 2005 .

[81]  Yeung Sam Hung,et al.  Distributed $H_{\infty}$ Filtering for Polynomial Nonlinear Stochastic Systems in Sensor Networks , 2011, IEEE Transactions on Industrial Electronics.

[82]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[83]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[84]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[85]  Zidong Wang,et al.  Distributed H∞ state estimation with stochastic parameters and nonlinearities through sensor networks: The finite-horizon case , 2012, Autom..

[86]  Guanrong Chen.  A simple treatment for suboptimal Kalman filtering in case of measurement data missing , 1990 .

[87]  Zidong Wang,et al.  A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[88]  Steven X. Ding,et al.  Optimal fault detection for linear discrete time-varying systems , 2010, Autom..

[89]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[90]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..

[91]  Zidong Wang,et al.  Distributed State Estimation for Discrete-Time Sensor Networks With Randomly Varying Nonlinearities and Missing Measurements , 2011, IEEE Transactions on Neural Networks.

[92]  Ben M. Chen,et al.  An Output Feedback Controller Design for Linear Systems Subject to Sensor Nonlinearities , 2003 .

[93]  Huijun Gao,et al.  On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays , 2012, Signal Process..

[94]  James Lam,et al.  Distributed ℋ ∞ filtering for repeated scalar nonlinear systems with random packet losses in sensor networks , 2011, Int. J. Syst. Sci..

[95]  B. Chen,et al.  Delay-Dependent Robust H∞ Control for T-S Fuzzy Systems With Time Delay , 2005, IEEE Trans. Fuzzy Syst..

[96]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[97]  Daniel W. C. Ho,et al.  Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case , 2010, IEEE Transactions on Signal Processing.

[98]  James Lam,et al.  $H_{\bm \infty}$ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements , 2009, IEEE Transactions on Fuzzy Systems.

[99]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[100]  H. Ye,et al.  Fault detection for Markovian jump systems , 2005 .

[101]  Samir Kouro,et al.  Unidimensional Modulation Technique for Cascaded Multilevel Converters , 2009, IEEE Transactions on Industrial Electronics.

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

[103]  Daniel W. C. Ho,et al.  Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations , 2010, IEEE Transactions on Automatic Control.

[104]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and L/sub 2/-disturbances , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[105]  Lv Liang,et al.  Analysis and design of singular linear systems under actuator saturation and L2/L∞ disturbances , 2008, 2008 27th Chinese Control Conference.

[106]  Dong Yue,et al.  Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[107]  Zidong Wang,et al.  On Nonlinear $H_{\infty }$ Filtering for Discrete-Time Stochastic Systems With Missing Measurements , 2008, IEEE Transactions on Automatic Control.

[108]  LamJames,et al.  A new delay system approach to network-based control , 2008 .

[109]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[110]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[111]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[112]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[113]  H. Karimi.  Robust H 1 Filter Design for Uncertain Linear Systems Over Network with Network-Induced Delays and Output Quantization , 2009 .

[114]  Steven X. Ding,et al.  Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems , 2007, Autom..