Nonfragile $H_{\infty}$ and $H_{2}$ Filter Designs for Continuous-Time Linear Systems Based on Randomized Algorithms

This paper investigates the problem of nonfragile H∞ and H2 filter designs for continuous-time linear systems. Additive filter gain variations to reflect the imprecision in filter implementation are considered. The nonfragile filter design is first formulated as a robust convex optimization problem. Then, both deterministic and randomized algorithms are employed to solve the obtained robust convex optimization problem. Compared with the deterministic algorithm, the proposed randomized one has two advantages: On one hand, it has acceptable computational complexity for systems with high dimensions; on the other hand, it can alleviate the conservatism of deterministic algorithms. Several examples are given to illustrate the effectiveness of the proposed method.

[1]  J. Geromel,et al.  H 2 and H ∞ Filtering Design Subject to Implementation Uncertainty , 2003 .

[2]  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.

[3]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[4]  Isaac Yaesh,et al.  Neuro-Adaptive $H_{\infty}$ Estimation and Its Application to Improved Tracking in GPS Receivers , 2009, IEEE Transactions on Industrial Electronics.

[5]  Ferrante Neri,et al.  Optimization of Delayed-State Kalman-Filter-Based Algorithm via Differential Evolution for Sensorless Control of Induction Motors , 2010, IEEE Transactions on Industrial Electronics.

[6]  B. A. Woodyatt,et al.  Fault Signatures Obtained From Fault Implant Tests on an F404 Engine , 1992 .

[7]  S. L. Ho,et al.  Speed estimation of an induction motor drive using an optimized extended Kalman filter , 2002, IEEE Trans. Ind. Electron..

[8]  Kiyoshi Ohishi,et al.  Kalman-Filter-Based Sensor Integration of Variable Power Assist Control Based on Human Stiffness Estimation , 2009, IEEE Transactions on Industrial Electronics.

[9]  Jianliang Wang,et al.  Robust nonfragile Kalman filtering for uncertain linear systems with estimator gain uncertainty , 2001, IEEE Trans. Autom. Control..

[10]  U. Shaked,et al.  Neuro-adaptive H∞ estimation and its application to improved tracking in GPS receivers , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[11]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[12]  M. Basin,et al.  Risk-Sensitive Approach to Optimal Filtering and Control for Linear Stochastic Systems , 2008, 2008 3rd International Conference on Innovative Computing Information and Control.

[13]  Young Soo Suh,et al.  Attitude Estimation by Multiple-Mode Kalman Filters , 2006, IEEE Transactions on Industrial Electronics.

[14]  Guang-Hong Yang,et al.  Insensitive Hinfinity filter design for continuous-time systems with respect to filter coefficient variations , 2010, Autom..

[15]  Wang Zhi-sheng.  Non-fragile H_∞ filtering for uncertain stochastic time-delay systems with Markovian jump parameters , 2010 .

[16]  Michael J. Grimble,et al.  Solution of the H∞ optimal linear filtering problem for discrete-time systems , 1990, IEEE Trans. Acoust. Speech Signal Process..

[17]  Edoardo Mosca,et al.  Robust H2 and Hinfinity filtering for uncertain linear systems , 2006, Autom..

[18]  Farid Golnaraghi,et al.  A Kalman/Particle Filter-Based Position and Orientation Estimation Method Using a Position Sensor/Inertial Measurement Unit Hybrid System , 2010, IEEE Transactions on Industrial Electronics.

[19]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[20]  Lihua Xie,et al.  H∞ estimation for uncertain systems , 1992 .

[21]  Sheng Chen,et al.  Robust Finite Word Length controller design , 2009, Autom..

[22]  Mickael Hilairet,et al.  Speed sensorless control of a DC-motor via adaptive filters , 2007 .

[23]  Michael V. Basin,et al.  Sub-optimal risk-sensitive filtering for third degree polynomial stochastic systems , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[24]  Bo Shen,et al.  Distributed H ∞ Filtering for Polynomial Systems in Sensor Networks , 2013 .

[25]  Magdi S. Mahmoud,et al.  Resilient linear filtering of uncertain systems , 2004, Autom..

[26]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

[27]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[28]  José Claudio Geromel,et al.  Suboptimal reduced-order filtering through an LMI-based method , 2006, IEEE Transactions on Signal Processing.

[29]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[30]  Maurício C. de Oliveira,et al.  H2 and Hinfinity Filtering Design Subject to Implementation Uncertainty , 2005, SIAM J. Control. Optim..

[31]  Semyon G. Rabinovich,et al.  Measurement Errors and Uncertainties: Theory and Practice , 1999 .

[32]  Biao Huang,et al.  Robust H2/H∞ filtering for linear systems with error variance constraints , 2000, IEEE Trans. Signal Process..

[33]  P. Dorato,et al.  Non-fragile controller design: an overview , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[34]  Gang Li,et al.  On the structure of digital controllers with finite word length consideration , 1998, IEEE Trans. Autom. Control..

[35]  Dah-Jing Jwo,et al.  An Adaptive Fuzzy Strong Tracking Kalman Filter for GPS/INS Navigation , 2007, IECON 2007 - 33rd Annual Conference of the IEEE Industrial Electronics Society.

[36]  Joseph R. Corrado,et al.  Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations , 2000 .

[37]  Thananchai Leephakpreeda,et al.  Sensorless DC motor drive via optimal observer‐based servo control , 2002 .

[38]  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.

[39]  Guang-Hong Yang,et al.  Non-fragile Hinfinity filter design for linear continuous-time systems , 2008, Autom..

[40]  Mickaël Hilairet,et al.  Speed and rotor flux estimation of induction machines using a two-stage extended Kalman filter , 2009, Autom..