The Smooth Variable Structure Filter This new method for estimating the motion of dynamic systems can compensate for sudden events such as fault conditions.

In this paper, a new method for state estimation, referred to as the smooth variable structure filter (SVSF), is presented. The SVSF method is model based and applies to smooth nonlinear dynamic systems. It allows for the explicit definition of the source of uncertainty and can guarantee stability given an upper bound for uncertainties and noise levels. The performance of the SVSF improves with more refined definition of upper bounds on parameter variations or uncertainties. Furthermore, most filtering methods provide as their measure of performance the filter innovation vector or (output) estimation error. However in addition to the innova- tion vector, the SVSF has a secondary set of performance indicators that correlate to the modeling errors specific to each state or parameter that is being estimated. The combined robustness and multiple indicators of performance allow for dynamic refinement of internal models in the SVSF. Dynamic refinement and robustness are features that are particularly advantageous in fault diagnosis and prediction. In this paper, the applications of the SVSF to linear and nonlinear systems, including one pertaining to fault detection, are provided. The characteristics of this filter in terms of its accuracy and rate of convergence are discussed.

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

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

[3]  R. Kochendörffer.  Kreyszig, E.: Advanced Engineering Mathematics. J. Wiley & Sons, Inc., New York, London 1962. IX + 856 S. 402 Abb. Preis s. 79.— , 1965 .

[4]  and Charles K. Taft Reswick,et al.  Introduction to Dynamic Systems , 1967 .

[5]  F. W. Kellaway,et al.  Advanced Engineering Mathematics , 1969, The Mathematical Gazette.

[6]  H. Sorenson.  Least-squares estimation: from Gauss to Kalman , 1970, IEEE Spectrum.

[7]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[8]  E Harth,et al.  Alopex: a stochastic method for determining visual receptive fields. , 1974, Vision research.

[9]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[10]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[11]  Thomas Kailath,et al.  Linear Systems , 1980 .

[12]  S. Drakunov.  Adaptive quasioptimal filter with discontinuous parameters , 1984 .

[13]  M. Corless,et al.  Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamical Systems via Continuous and Discontinuous Feedback Control , 1984 .

[14]  Jean-Jacques E. Slotine,et al.  Sliding controller design for non-linear systems , 1984 .

[15]  Simon Haykin,et al.  Introduction to Adaptive Filters , 1984 .

[16]  Jean-Jacques E. Slotine,et al.  The Robust Control of Robot Manipulators , 1985 .

[17]  Ümit Özgüner,et al.  A decentralized variable structure control algorithm for robotic manipulators , 1985, IEEE J. Robotics Autom..

[18]  Hansruedi Bühler.  Réglage par mode de glissement , 1986 .

[19]  J. Hedrick,et al.  Nonlinear state estimation using sliding observers , 1986, 1986 25th IEEE Conference on Decision and Control.

[20]  Peter A. Cook,et al.  Nonlinear dynamical systems , 1986 .

[21]  A. Arapostathis,et al.  Simple sliding mode control scheme applied to robot manipulators , 1987 .

[22]  S. Żak,et al.  State observation of nonlinear uncertain dynamical systems , 1987 .

[23]  S. Żak,et al.  Comparative study of non-linear state-observation techniques , 1987 .

[24]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[25]  Y. P. Chen,et al.  A new controller design for manipulators using the theory of variable structure systems , 1988 .

[26]  Stanislaw H. Zak,et al.  Combined observer-controller synthesis for uncertain dynamical systems with applications , 1988, IEEE Trans. Syst. Man Cybern..

[27]  Jean-Jacques E. Slotine,et al.  Robot analysis and control , 1988, Autom..

[28]  C. Dorling,et al.  Robust hyperplane design in multivariable variable structure control systems , 1988 .

[29]  A. Zinober.  Deterministic control of uncertain systems , 1989, Proceedings. ICCON IEEE International Conference on Control and Applications.

[30]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[31]  R. J. Richards,et al.  Sliding mode control of an electrically powered industrial robot , 1992 .

[32]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[33]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[34]  Benito R. Fernandez,et al.  Robust fault detection in nonlinear systems using sliding mode observers , 1993, Proceedings of IEEE International Conference on Control and Applications.

[35]  Okyay Kaynak,et al.  Discrete-time sliding mode control in the presence of system uncertainty , 1993 .

[36]  Abhijit S. Pandya,et al.  A recurrent neural network controller and learning algorithm for the on-line learning control of autonomous underwater vehicles , 1994, Neural Networks.

[37]  S. Spurgeon,et al.  On the development of discontinuous observers , 1994 .

[38]  Vadim I. Utkin,et al.  Adaptive sliding mode control in discrete-time systems , 1995, Autom..

[39]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[40]  V. Utkin,et al.  Discrete-event sliding mode observers for continuous-time systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[41]  M. Tomizuka,et al.  Robust control of discretized continuous systems using the theory of sliding modes , 1995 .

[42]  Masoud Khoshzaban-Zavarehi,et al.  On-line condition monitoring and fault diagnosis in hydraulic system components using parameter estimation and pattern classification , 1997 .

[43]  R. Decarlo,et al.  Discrete-time/discrete-event sliding mode design via Lyapunov approach , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[44]  Vadim I. Utkin,et al.  Variable structure control for uncertain sampled data systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[45]  V. Utkin,et al.  Sliding mode control design based on Ackermann's formula , 1998, IEEE Trans. Autom. Control..

[46]  I. Haskara.  On sliding mode observers via equivalent control approach , 1998 .

[47]  Tong Heng Lee,et al.  On the design of a nonlinear adaptive variable structure derivative estimator , 2000, IEEE Trans. Autom. Control..

[48]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[49]  Mehrdad Saif,et al.  Sliding-mode observer for uncertain systems. II. Nonlinear systems case , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[50]  Andrew A. Goldenberg,et al.  Design of a new high-performance electrohydraulic actuator , 2000 .

[51]  Rolf Isermann,et al.  Hierarchical motor diagnosis utilizing structural knowledge and a self-learning neuro-fuzzy scheme , 2000, IEEE Trans. Ind. Electron..

[52]  Sarah K. Spurgeon,et al.  Sliding mode observers for fault detection and isolation , 2000, Autom..

[53]  Yaodong Pan,et al.  Variable structure control with sliding sector , 2000, Autom..

[54]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[55]  Vadim I. Utkin,et al.  Developing a fault tolerant power-train control system by integrating design of control and diagnostics , 2001 .

[56]  Rolf Isermann,et al.  Diagnosis Methods for Electronic Controlled Vehicles , 2001 .

[57]  J. K. Hedrick,et al.  Disturbance Adaptive Discrete-Time Sliding Control With Application to Engine Speed Control , 2001 .

[58]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[59]  F. Lamnabhi-Lagarrigue,et al.  Parametric identification methodology using sliding modes observer , 2001 .

[60]  K. B. Goh,et al.  Fault diagnostics using sliding mode techniques , 2002 .

[61]  Nariman Sepehri,et al.  Parametric fault diagnosis for electrohydraulic cylinder drive units , 2002, IEEE Trans. Ind. Electron..

[62]  Alan Solon Ivor Zinober,et al.  Sliding mode state observers for discrete-time linear systems , 2002, Int. J. Syst. Sci..

[63]  S. Habibi,et al.  The Variable Structure Filter , 2003 .

[64]  Didier Maquin,et al.  Sliding mode multiple observer for fault detection and isolation , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[65]  T. Floquet *,et al.  On the robust fault detection via a sliding mode disturbance observer , 2004 .

[66]  Yunsong Wang,et al.  Application of non-linear observers to on-line estimation of indicated torque in automotive engines , 2005 .

[67]  S. Geer.  Least Squares Estimation , 2005 .

[68]  W. Lohmiller,et al.  Contraction analysis of non-linear distributed systems , 2005 .