Event-driven boundary control for time fractional diffusion systems under time-varying input disturbance

This paper is concerned with the event-driven boundary state feedback control problem for the subdiffusion processes governed by time fractional diffusion systems with unknown time-varying input disturbance. To evaluate the unknown disturbance, we propose an estimator through filtering, which only requires that the Laplace transformation of the disturbance signal exists and is finite. Moreover, we study the stability of the closed-loop system using a state feedback event-driven control strategic via Backstepping technique. A positive lower bounded minimum inter-event time of the event-driven strategic is then presented to avoid the occurrence of Zeno phenomenon. Finally, we work out a numerical example to test the proposed method.

[1]  Wu-Chung Su,et al.  Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties , 2011, Autom..

[2]  T. A. Burton,et al.  Fractional differential equations and Lyapunov functionals , 2011 .

[3]  YangQuan Chen,et al.  Boundary feedback stabilisation for the time fractional-order anomalous diffusion system , 2016 .

[4]  Wayne E. Stark,et al.  Low-energy wireless communication network design , 2002, IEEE Wirel. Commun..

[5]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[6]  Vladimir V. Uchaikin,et al.  Fractional theory for transport in disordered semiconductors , 2008 .

[7]  Beibei Ren,et al.  Robust Control for a Class of Nonaffine Nonlinear Systems Based on the Uncertainty and Disturbance Estimator , 2015, IEEE Transactions on Industrial Electronics.

[8]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[9]  Fei Hao,et al.  Event-triggered average consensus control for discrete-time multi-agent systems , 2012 .

[10]  S. Wearne,et al.  Fractional Reaction-Diffusion , 2000 .

[11]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[12]  M. Weiss,et al.  Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. , 2004, Biophysical journal.

[13]  YangQuan Chen,et al.  Actuator characterisations to achieve approximate controllability for a class of fractional sub-diffusion equations , 2017, Int. J. Control.

[14]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[15]  Beibei Ren,et al.  UDE-based Robust Boundary Control of Heat Equation with Unknown Input Disturbance , 2017 .

[16]  Yangquan Chen,et al.  Regional controllability analysis of fractional diffusion equations with Riemann-Liouville time fractional derivatives , 2016, Autom..

[17]  YangQuan Chen,et al.  Cyber-physical systems as general distributed parameter systems: three types of fractional order models and emerging research opportunities , 2015, IEEE/CAA Journal of Automatica Sinica.

[18]  Qing-Chang Zhong,et al.  Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator , 2004 .

[19]  Santos B. Yuste,et al.  Subdiffusion-limited A+A reactions. , 2001 .

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

[21]  Hongye Su,et al.  Event-Triggered Adaptive Control for a Class of Uncertain Nonlinear Systems , 2017, IEEE Transactions on Automatic Control.

[22]  Jun-Min Wang,et al.  Active disturbance rejection control and sliding mode control of one-dimensional unstable heat equation with boundary uncertainties , 2015, IMA J. Math. Control. Inf..

[23]  Qing-Long Han,et al.  An Overview and Deep Investigation on Sampled-Data-Based Event-Triggered Control and Filtering for Networked Systems , 2017, IEEE Transactions on Industrial Informatics.

[24]  Manuel Mazo,et al.  An ISS self-triggered implementation of linear controllers , 2009, Autom..

[25]  Sandrine Lyonnard,et al.  Water sub-diffusion in membranes for fuel cells , 2017, Scientific Reports.

[26]  M. Krstić.  Boundary Control of PDEs: A Course on Backstepping Designs , 2008 .

[27]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[28]  Antonios Armaou,et al.  Feedback control of dissipative PDE systems in the presence of uncertainty and noise using extended Kalman filter , 2009, 2009 American Control Conference.

[29]  M. Yasui,et al.  Origin of subdiffusion of water molecules on cell membrane surfaces , 2014, Scientific Reports.

[30]  Dong Yue,et al.  Communication and Control for Networked Complex Systems , 2015 .