Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the joint state filtering and parameter estimation problem for linear stochastic time-delay systems with unknown parameters. The original problem is reduced to the mean-square filtering problem for incompletely measured bilinear time-delay system states over linear observations. The unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. To deal with the new filtering problem, the paper designs the mean-square finite-dimensional filter for incompletely measured bilinear time-delay system states over linear observations. A closed system of the filtering equations is then derived for a bilinear time-delay state over linear observations. Finally, the paper solves the original joint estimation problem. The obtained solution is based on the designed mean-square filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the filter for the extended state vector also serves as the identifier for the unknown parameters. In the example, performance of the designed state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations.

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

[2]  Chin Wen Liao,et al.  A DELAY-DEPENDENT APPROACH TO DESIGN STATE ESTIMATOR FOR DISCRETE STOCHASTIC RECURRENT NEURAL NETWORK WITH INTER V AL TIME-V ARYING DELAYS , 2009 .

[3]  M. Basin,et al.  Optimal filtering for linear systems with state and observation delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[5]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[6]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[7]  Pedro Luis Dias Peres,et al.  Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays , 2001, IEEE Trans. Signal Process..

[8]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

[9]  H. Kushner.  On the Differential Equations Satisfied by Conditional Probablitity Densities of Markov Processes, with Applications , 1964 .

[10]  Shengyuan Xu,et al.  Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty , 2002 .

[11]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[12]  W. Wonham.  Some applications of stochastic difierential equations to optimal nonlinear ltering , 1964 .

[13]  M. Basin.  New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems , 2008 .

[14]  V. Pugachev,et al.  Stochastic Systems: Theory and Applications , 2002 .

[15]  Michael V. Basin,et al.  Optimal filtering for linear state delay systems , 2005, IEEE Transactions on Automatic Control.

[16]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[17]  M. Basin,et al.  Optimal Filtering for Incompletely Measured Polynomial States over Linear Observations , 2008, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[18]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[19]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

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

[21]  Aria Alasty,et al.  Adaptive robust attitude control of a flexible spacecraft , 2006 .

[22]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[23]  Daizhan Cheng,et al.  Optimal estimation for continuous-time systems with delayed measurements , 2006, IEEE Trans. Autom. Control..

[24]  J. Lam,et al.  A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain distributed delay systems , 2005, IEEE Transactions on Signal Processing.

[25]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[26]  Ligang Wu,et al.  Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay , 2009, Signal Process..

[27]  James Lam,et al.  Nonlinear filtering for state delayed systems with Markovian switching , 2003, IEEE Trans. Signal Process..

[28]  M. Basin,et al.  Optimal linear filtering over observations with multiple delays , 2004 .

[29]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

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

[31]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..

[32]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[33]  Michael V. Basin,et al.  Alternative optimal filter for linear systems with multiple state and observation delays , 2008, 2008 47th IEEE Conference on Decision and Control.

[34]  Lihua Xie,et al.  Control and estimation of systems with input/output delays , 2007 .

[35]  M. Basin,et al.  Optimal filtering for polynomial system states with polynomial multiplicative noise , 2006, 2006 American Control Conference.

[36]  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.

[37]  Jie Sheng,et al.  Optimal filtering for multirate systems , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  V. Benes.  Exact finite-dimensional filters for certain diffusions with nonlinear drift , 1981 .

[39]  Emilia Fridman,et al.  An improved delay-dependent H∞ filtering of linear neutral systems , 2004, IEEE Trans. Signal Process..

[40]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[41]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[42]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[43]  Huijun Gao,et al.  Induced l/sub 2/ and generalized H/sub 2/ filtering for systems with repeated scalar nonlinearities , 2005, IEEE Transactions on Signal Processing.

[44]  M. Mahmoud,et al.  Robust Kalman filtering for continuous time-lag systems with Markovian jump parameters , 2003 .

[45]  Zidong Wang,et al.  H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays , 2009, Autom..

[46]  Huijun Gao,et al.  Filtering for uncertain 2-D discrete systems with state delays , 2007, Signal Process..

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