Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

In this article, the robust trajectory tracking problem of iterative learning control (ILC) for uncertain nonlinear systems is considered, and the effects from locally Lipschitz nonlinearities, input saturations, and nonzero system relative degrees are treated. A saturated ILC algorithm is given, with the convergence analysis exploited using a composite energy function-based approach. It is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly. Furthermore, the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations. Two examples are given to demonstrate the validity of saturated ILC for systems with the relative degree of one, input saturation, and locally Lipschitz nonlinearity.

[1]  Xinghuo Yu,et al.  Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Miroslav Krstic,et al.  Iterative learning control based on extremum seeking , 2016, Autom..

[3]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.

[4]  Shangtai Jin,et al.  Computationally Efficient Data-Driven Higher Order Optimal Iterative Learning Control , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[6]  Emre Kural,et al.  96 A Survey of Iterative Learning Control Al earning-based method for high-performance tracking control , 2006 .

[7]  Ying Tan,et al.  On P-type iterative learning control for nonlinear systems without global Lipschitz continuity condition , 2015, 2015 American Control Conference (ACC).

[8]  Zhongsheng Hou,et al.  Adaptive Iterative Learning Control for High-Speed Trains With Unknown Speed Delays and Input Saturations , 2016, IEEE Transactions on Automation Science and Engineering.

[9]  Ying Tan,et al.  Convergence analysis of feedback-based iterative learning control with input saturation , 2019, Autom..

[10]  Xuhui Bu,et al.  RBFNN-Based Data-Driven Predictive Iterative Learning Control for Nonaffine Nonlinear Systems , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Xuefang Li,et al.  Adaptive Boundary Iterative Learning Control for an Euler–Bernoulli Beam System With Input Constraint , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Chiang-Ju Chien,et al.  Further results on adaptive iterative learning control of robot manipulators , 2008, Autom..

[13]  Jian-Xin Xu,et al.  A survey on iterative learning control for nonlinear systems , 2011, Int. J. Control.

[14]  John Hauser,et al.  Learning control for a class of nonlinear systems , 1987, 26th IEEE Conference on Decision and Control.

[15]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[16]  Kira Barton,et al.  Exponential stability of nonlinear differential repetitive processes with applications to iterative learning control , 2017, Autom..

[17]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[18]  Mingxuan Sun,et al.  Neural AILC for Error Tracking Against Arbitrary Initial Shifts , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Jinde Cao,et al.  Synchronous and Asynchronous Iterative Learning Strategies of T–S Fuzzy Systems With Measurable and Unmeasurable State Information , 2018, IEEE Transactions on Fuzzy Systems.

[20]  Miao Yu,et al.  Composite Energy Function-Based Spatial Iterative Learning Control in Motion Systems , 2018, IEEE Transactions on Control Systems Technology.

[21]  W. Rudin.  Principles of mathematical analysis , 1964 .

[22]  Radu-Emil Precup,et al.  Model-Free Primitive-Based Iterative Learning Control Approach to Trajectory Tracking of MIMO Systems With Experimental Validation , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Dong Shen,et al.  Performance Enhancement of Learning Tracking Systems Over Fading Channels With Multiplicative and Additive Randomness , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Danwei Wang,et al.  Enhanced Data-Driven Optimal Terminal ILC Using Current Iteration Control Knowledge , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Ying Tan,et al.  A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties , 2002, IEEE Trans. Autom. Control..

[26]  Xiao-Dong Li,et al.  HONN-Based Adaptive ILC for Pure-Feedback Nonaffine Discrete-Time Systems With Unknown Control Directions , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Kevin L. Moore,et al.  Robust cooperative learning control for directed networks with nonlinear dynamics , 2017, Autom..

[28]  Xuhui Bu,et al.  Adaptive Iterative Learning Control for Linear Systems With Binary-Valued Observations , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Junmin Li,et al.  Adaptive iterative learning control for coordination of second‐order multi‐agent systems , 2014 .

[30]  Dong Shen.  Data-Driven Learning Control for Stochastic Nonlinear Systems: Multiple Communication Constraints and Limited Storage , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Mingxuan Sun,et al.  A Barbalat-Like Lemma with Its Application to Learning Control , 2009, IEEE Transactions on Automatic Control.

[32]  Shangtai Jin,et al.  A unified data-driven design framework of optimality-based generalized iterative learning control , 2015, Comput. Chem. Eng..

[33]  Zongcheng Liu,et al.  Initial states iterative learning for three-dimensional ballistic endpoint control , 2017, Memetic Comput..

[34]  Deyuan Meng,et al.  Deterministic Convergence for Learning Control Systems Over Iteration-Dependent Tracking Intervals , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Dong Shen,et al.  Iterative Learning Control for Multi-agent Systems Coordination , 2017 .

[36]  Xu Jin,et al.  Iterative learning control for non‐repetitive trajectory tracking of robot manipulators with joint position constraints and actuator faults , 2017 .

[37]  Deyuan Meng,et al.  Contraction Mapping-Based Robust Convergence of Iterative Learning Control With Uncertain, Locally Lipschitz Nonlinearity , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[38]  Chiang-Ju Chien,et al.  A Unified Adaptive Iterative Learning Control Framework for Uncertain Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[39]  Dong Shen,et al.  Adaptive Learning Control for Nonlinear Systems With Randomly Varying Iteration Lengths , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Mingxuan Sun,et al.  Closed‐loop iterative learning control for non‐linear systems with initial shifts , 2002 .

[41]  Dong Shen,et al.  Multidimensional Gains for Stochastic Approximation , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Biao Huang,et al.  3-D Learning-Enhanced Adaptive ILC for Iteration-Varying Formation Tasks , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Deyuan Meng,et al.  Iterative Learning Control for Continuous-Time Systems with Locally Lipschitz Nonlinearity and Input Saturation , 2018, 2018 IEEE 7th Data Driven Control and Learning Systems Conference (DDCLS).

[45]  Deyuan Meng,et al.  Convergence Conditions for Solving Robust Iterative Learning Control Problems Under Nonrepetitive Model Uncertainties , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[46]  P. Olver.  Nonlinear Systems , 2013 .

[47]  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).