State estimation of nonlinear fractional order system with Lévy noises by using EKF

In this paper, the state estimation problem is discussed for discrete nonlinear fractional order system with non-Gaussian Lévy noises. By disposing the non-Gaussian Lévy noises, the system state vector and measurement vector can be approximated directly, which could enable to deduce the new system noise covariance matrix and measurement noise covariance matrix, respectively. Based on the proposed approximating method, a novel fractional order extended Kalman filter (EKF) designing strategy is developed for discrete nonlinear fractional order system with non-Gaussian Lévy noises, which is more general and effective than some existing results. Finally, some simulation results are provided to verify and illustrate the effectiveness of the obtain results.

[1]  D. Applebaum.  Lévy Processes and Stochastic Calculus: Preface , 2009 .

[2]  Ning Li,et al.  Robust H∞ load frequency control of delayed multi-area power system with stochastic disturbances , 2016, Neurocomputing.

[3]  Yan Xu,et al.  Reactive power planning under high penetration of wind energy using Benders decomposition , 2015 .

[4]  Jinde Cao,et al.  Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks , 2015, Neurocomputing.

[5]  S. Ghasemi,et al.  Application of Fractional Calculus Theory to Robust Controller Design for Wind Turbine Generators , 2014, IEEE Transactions on Energy Conversion.

[6]  Zidong Wang,et al.  On Nonlinear $H_{\infty }$ Filtering for Discrete-Time Stochastic Systems With Missing Measurements , 2008, IEEE Transactions on Automatic Control.

[7]  Ning Li,et al.  Robust stochastic stability of power system with time-varying delay under Gaussian random perturbations , 2015, Neurocomputing.

[8]  Zidong Wang,et al.  Distributed State Estimation for Discrete-Time Sensor Networks With Randomly Varying Nonlinearities and Missing Measurements , 2011, IEEE Transactions on Neural Networks.

[9]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[10]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[11]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[12]  Jun Xiao,et al.  Sizing of Energy Storage and Diesel Generators in an Isolated Microgrid Using Discrete Fourier Transform (DFT) , 2014, IEEE Transactions on Sustainable Energy.

[13]  Jinde Cao,et al.  Robust stochastic stability analysis of genetic regulatory networks with disturbance attenuation , 2012, Neurocomputing.

[14]  Hongbin Sun,et al.  Interval optimization based operating strategy for gas-electricity integrated energy systems considering demand response and wind uncertainty , 2016 .

[15]  Nils Hoffmann,et al.  Minimal Invasive Equivalent Grid Impedance Estimation in Inductive–Resistive Power Networks Using Extended Kalman Filter , 2014, IEEE Transactions on Power Electronics.

[16]  Wei Xing Zheng,et al.  L2-L∞ filtering for stochastic Markovian jump delay systems with nonlinear perturbations , 2015, Signal Process..

[17]  Fangxing Li,et al.  Coupon-Based Demand Response Considering Wind Power Uncertainty: A Strategic Bidding Model for Load Serving Entities , 2016, IEEE Transactions on Power Systems.

[18]  David Applebaum,et al.  Lévy Processes and Stochastic Calculus by David Applebaum , 2009 .

[19]  Z. Q. Chen,et al.  Chaotic Characteristics Analysis and Circuit Implementation for a Fractional-Order System , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Fangxing Li,et al.  Strategic scheduling of energy storage for load serving entities in locational marginal pricing market , 2016 .

[21]  Fangxing Li,et al.  Evaluation of LMP Intervals Considering Wind Uncertainty , 2016, IEEE Transactions on Power Systems.

[22]  Shouming Zhong,et al.  Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems , 2014, Autom..

[23]  Hongbin Sun,et al.  Robust mean-variance optimization model for grid-connected microgrids , 2015, 2015 IEEE Power & Energy Society General Meeting.

[24]  Ahmet Dumlu,et al.  Trajectory Tracking Control for a 3-DOF Parallel Manipulator Using Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ Control , 2014, IEEE Transactions on Industrial Electronics.

[25]  D. Sierociuk,et al.  Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation , 2006 .

[26]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[27]  Ming Ni,et al.  A modified Kalman filter algorithm for fractional system under Lévy noises , 2015, J. Frankl. Inst..

[28]  Mehmet Önder Efe,et al.  Fractional Order Systems in Industrial Automation—A Survey , 2011, IEEE Transactions on Industrial Informatics.

[29]  Adriano Fagiolini,et al.  Convergence Analysis of Extended Kalman Filter for Sensorless Control of Induction Motor , 2015, IEEE Transactions on Industrial Electronics.

[30]  Eric Monmasson,et al.  Dual-Kalman-Filter-Based Identification and Real-Time Optimization of PV Systems , 2015, IEEE Transactions on Industrial Electronics.

[31]  Fangxing Li,et al.  Strategic CBDR bidding considering FTR and wind power , 2016 .

[32]  H. Salarieh,et al.  On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment , 2014 .

[33]  J. L. Lage,et al.  Application of Fractional Calculus to Fluid Mechanics , 2002 .

[34]  M. V. Kulikova,et al.  Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter , 2014, IEEE Transactions on Automatic Control.

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

[36]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.