A Novel Markov Chain Based ILC Analysis for Linear Stochastic Systems Under General Data Dropouts Environments

This technical note contributes to the convergence analysis for iterative learning control (ILC) for linear stochastic systems under general data dropout environments, i.e., data dropouts occur randomly at both the measurement and actuator sides. Data updating in the memory array is arranged in such a way that data at every time instance is updated independently, which allows successive data dropouts both in time and iteration axes. The update mechanisms for both the computed input and real input are proposed and then the update process of both inputs is shown to be a Markov chain. By virtue of Markov modeling, a new analysis method is developed to prove the convergence in both mean square and almost sure senses. An illustrative example verifies the theoretical results.

[1]  Dong Shen,et al.  ILC for networked nonlinear systems with unknown control direction through random Lossy channel , 2015, Syst. Control. Lett..

[2]  Xuefang Li,et al.  Precise Speed Tracking Control of a Robotic Fish Via Iterative Learning Control , 2016, IEEE Transactions on Industrial Electronics.

[3]  Yang Shi,et al.  Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains , 2009, IEEE Transactions on Automatic Control.

[4]  Jun Wu,et al.  Iterative Learning Control for Remote Control Systems with Communication Delay and Data Dropout , 2012 .

[5]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[6]  Kevin L. Moore,et al.  Stability of discrete-time iterative learning control with random data dropouts and delayed controlled signals in networked control systems , 2008, 2008 10th International Conference on Control, Automation, Robotics and Vision.

[7]  Jian Liu,et al.  Networked iterative learning control approach for nonlinear systems with random communication delay , 2016, Int. J. Syst. Sci..

[8]  Dong Shen,et al.  Survey on stochastic iterative learning control , 2014 .

[9]  Chongzhao Han,et al.  Multiple Maneuvering Target Tracking by Improved Particle Filter Based on Multiscan JPDA , 2012 .

[10]  Dong Shen,et al.  Iterative learning control for networked stochastic systems with random packet losses , 2014, Int. J. Control.

[11]  Miao Yu,et al.  A high-order internal model based iterative learning control scheme for discrete linear time-varying systems , 2015, Int. J. Autom. Comput..

[12]  Xuhui Bu,et al.  H∞ iterative learning controller design for a class of discrete-time systems with data dropouts , 2014, Int. J. Syst. Sci..

[13]  Xuhui Bu,et al.  Iterative learning control for a class of nonlinear systems with random packet losses , 2013 .

[14]  YangQuan Chen,et al.  Intermittent iterative learning control , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[15]  Ya-Jun Pan,et al.  Effects of network communications on a class of learning controlled non-linear systems , 2009, Int. J. Syst. Sci..

[16]  Samer S. Saab.  Selection of the learning gain matrix of an iterative learning control algorithm in presence of measurement noise , 2005, IEEE Transactions on Automatic Control.

[17]  Krzysztof Galkowski,et al.  Stability of nonlinear discrete repetitive processes with Markovian switching , 2015, Syst. Control. Lett..

[18]  Keyou You,et al.  Minimum Data Rate for Mean Square Stabilizability of Linear Systems With Markovian Packet Losses , 2011, IEEE Transactions on Automatic Control.

[19]  Yong Fang,et al.  Convergence Analysis of Wireless Remote Iterative Learning Control Systems with Dropout Compensation , 2013 .

[20]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[21]  Kevin L. Moore,et al.  Discrete-time Intermittent Iterative Learning Controller with Independent Data Dropouts , 2008 .

[22]  Jian-Xin Xu,et al.  High-Performance Tracking of Piezoelectric Positioning Stage Using Current-Cycle Iterative Learning Control With Gain Scheduling , 2014, IEEE Transactions on Industrial Electronics.

[23]  Xuhui Bu,et al.  Stability of first and high order iterative learning control with data dropouts , 2011 .

[24]  Samer S. Saab,et al.  A discrete-time stochastic learning control algorithm , 2001, IEEE Trans. Autom. Control..

[25]  P. Caines.  Linear Stochastic Systems , 1988 .

[26]  Kevin L. Moore,et al.  Iterative Learning Control: Brief Survey and Categorization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).