Tracking Differentiator Based Fractional Order Model Reference Adaptive Control: The 1 < α < 2 Case

This article investigates the problem of model reference adaptive control for a class of fractional order linear and nonlinear systems. Based on the fractional order tracking differentiator, the reference model adaptive control scheme is extended to the fractional order systems with the commensurate order 1 <; α <; 2. The stability of closed-loop control system is analyzed using frequency distributed model and Lyapunov stability theorem. Moreover, numerical simulations are performed to demonstrate the effectiveness of the proposed method.

[1]  Wang Yong.  Improved linear matrix inequalities stability criteria for fractional order systems and robust stabilization synthesis:The 0 , 2013 .

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

[3]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[4]  Alain Oustaloup,et al.  A Lyapunov approach to the stability of fractional differential equations , 2009, Signal Process..

[5]  Dominik Sierociuk,et al.  Adaptive Feedback Control of Fractional Order Discrete State-Space Systems , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[6]  Bao Shi,et al.  On Fractional Model Reference Adaptive Control , 2014, TheScientificWorldJournal.

[7]  Ruoxun Zhang,et al.  Adaptive synchronization of fractional-order chaotic systems via a single driving variable , 2011 .

[8]  Yong Wang,et al.  Frequency domain subspace identification of commensurate fractional order input time delay systems , 2011 .

[9]  Maamar Bettayeb,et al.  A NOTE ON THE CONTROLLABILITY AND THE OBSERVABILITY OF FRACTIONAL DYNAMICAL SYSTEMS , 2006 .

[10]  Samir Ladaci,et al.  Fractional order adaptive high-gain controllers for a class of linear systems , 2008 .

[11]  Alain Oustaloup,et al.  The CRONE Control of Resonant Plants: Application to a Flexible Transmission , 1995, Eur. J. Control.

[12]  Yong Wang,et al.  Subspace identification for fractional order Hammerstein systems based on instrumental variables , 2012 .

[13]  Wang Li,et al.  Robust stability analysis for a class of fractional order systems with uncertain parameters , 2011, J. Frankl. Inst..

[14]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications , 2011 .

[15]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing , 2012 .

[16]  Alain Oustaloup,et al.  Transients of fractional-order integrator and derivatives , 2012, Signal Image Video Process..

[17]  Yong Wang,et al.  A rational approximate method to fractional order systems , 2014 .

[18]  Zhen Wang,et al.  Control of an uncertain fractional order economic system via adaptive sliding mode , 2012, Neurocomputing.

[19]  Alain Oustaloup,et al.  State variables and transients of fractional order differential systems , 2012, Comput. Math. Appl..

[20]  Samir Ladaci,et al.  On Fractional Adaptive Control , 2006 .

[21]  Wenqiang Ji,et al.  Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems , 2013 .