Linear estimator for fractional systems

We address the issue of state estimation of nonlinear incommensurate fractional-order systems via linear observer in this paper. The basic idea is proposed under a synchronization framework which makes the response system a linear observer for the state of the drive system. By developing this approach, a linear time-invariant synchronization error system is obtained, and stability analysis is relied on the theory of linear incommensurate fractional-order systems. The suggested tool proves to be effective and systematic in achieving global synchronization. Simulation results verify and illustrate the effectiveness of the proposed method on some new fractional-order hyperchaotic systems.

[1]  Manuel Duarte Ortigueira,et al.  Identifying a Transfer Function From a Frequency Response , 2007 .

[2]  Hongtao Lu,et al.  Synchronization of a new fractional-order hyperchaotic system , 2009 .

[3]  Manuel Duarte Ortigueira.  A new symmetric fractional B-spline , 2003, Signal Process..

[4]  Tiegang Gao,et al.  Adaptive synchronization of a new hyperchaotic system with uncertain parameters , 2007 .

[5]  José António Tenreiro Machado,et al.  A fractional approach for the motion planning of redundant and hyper-redundant manipulators , 2011, Signal Process..

[6]  José António Tenreiro Machado,et al.  Fractional signals and systems , 2011, Signal Process..

[7]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[8]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[9]  Manuel Ortigueira,et al.  Special Issue on Fractional signal Processing and applications , 2003 .

[10]  M. Caputo.  Linear models of dissipation whose Q is almost frequency independent , 1966 .

[11]  Jinhu Lü,et al.  Stability analysis of linear fractional differential system with multiple time delays , 2007 .

[12]  Yao-Lin Jiang,et al.  Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal , 2008 .

[13]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .

[14]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[15]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[16]  Dominik Sierociuk,et al.  Improved fractional Kalman filter and its application to estimation over lossy networks , 2011, Signal Process..

[17]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[18]  Jian S. Dai,et al.  Robotics: State of the Art and Future Trends , 2013 .

[19]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[20]  I. Podlubny.  Fractional differential equations , 1998 .

[21]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[22]  Miguel Romero,et al.  Arbitrary real-order cost functions for signals and systems , 2011, Signal Process..

[23]  Y. Q. Chen,et al.  Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control , 2002 .

[24]  Dequan Li,et al.  A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems , 2010 .

[25]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[26]  Reza Ghaderi,et al.  Fuzzy fractional order sliding mode controller for nonlinear systems , 2010 .

[27]  Reply to “Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978” ” , 2012 .

[28]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[29]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[30]  Junwei Wang,et al.  Designing synchronization schemes for chaotic fractional-order unified systems , 2006 .

[31]  Y. Chen,et al.  Fractional Order Disturbance Observer for Robust Vibration Suppression , 2004 .

[32]  Sara Dadras,et al.  Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system , 2010 .

[33]  Mohammad Saleh Tavazoei,et al.  Notes on integral performance indices in fractional-order control systems , 2010 .

[34]  José António Tenreiro Machado,et al.  Fractional calculus applications in signals and systems , 2006, Signal Processing.

[35]  Yangquan Chen,et al.  A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments , 2010, IEEE Transactions on Control Systems Technology.

[36]  H. Srivastava,et al.  THEORY AND APPLICATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS. NORTH-HOLLAND MATHEMATICS STUDIES , 2006 .

[37]  Alain Oustaloup,et al.  Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation , 1981 .

[38]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[39]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[40]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[41]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[42]  F. Mainardi.  Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[43]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[44]  Vicente Feliú Batlle,et al.  Fractional order control strategies for power electronic buck converters , 2006, Signal Process..

[45]  Weihua Deng,et al.  Synchronization of Chaotic Fractional Chen System , 2005 .

[46]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[47]  LJubisa Stankovic,et al.  Fractional Fourier transform as a signal processing tool: An overview of recent developments , 2011, Signal Process..

[48]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[49]  Mohammad Saleh Tavazoei,et al.  Comments on “Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control” [Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] , 2011 .