Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

Abstract In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.

[1]  Jing Wang,et al.  Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems , 2020, Appl. Math. Comput..

[2]  S. Lakshmanan,et al.  Nonfragile Sampled-Data Control for Uncertain Networked Control Systems With Additive Time-Varying Delays , 2019, IEEE Transactions on Cybernetics.

[3]  Salvatore Monaco,et al.  Lyapunov design under sampling for a synchronous machine , 2009, 2009 European Control Conference (ECC).

[4]  Dragan Nesic,et al.  Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation , 2005, Autom..

[5]  Michael Malisoff,et al.  Stabilization of Nonlinear Time-Varying Systems Through a New Prediction Based Approach , 2017, IEEE Transactions on Automatic Control.

[6]  Jian Guo,et al.  Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay , 2019, J. Frankl. Inst..

[7]  Jinde Cao,et al.  An Improved Result on Sampled-Data Synchronization of Markov Jump Delayed Neural Networks , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Valentin Tanasa,et al.  Backstepping Control Under Multi-Rate Sampling , 2016, IEEE Transactions on Automatic Control.

[9]  Guang-Hong Yang,et al.  Event-based reduced-order fuzzy filtering for networked control systems with time-varying delays , 2019, Appl. Math. Comput..

[10]  Xue-Jun Xie,et al.  Global Adaptive Stabilization and Tracking Control for High-Order Stochastic Nonlinear Systems With Time-Varying Delays , 2018, IEEE Transactions on Automatic Control.

[11]  Xiao-Heng Chang,et al.  Fuzzy Peak-to-Peak Filtering for Networked Nonlinear Systems With Multipath Data Packet Dropouts , 2019, IEEE Transactions on Fuzzy Systems.

[12]  Hassan K. Khalil,et al.  Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[13]  Jin Bae Park,et al.  An improved digital redesign for sampled-data fuzzy control systems: Fuzzy Lyapunov function approach , 2017, Inf. Sci..

[14]  Eduardo Sontag,et al.  Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems , 1999 .

[15]  Gang Feng,et al.  Sampled‐data control of nonlinear networked systems with time‐delay and quantization , 2016 .

[16]  Dorothée Normand-Cyrot,et al.  Issues on Nonlinear Digital Control , 2001, Eur. J. Control.

[17]  Kemei Zhang,et al.  Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems With FT-SISS Inverse Dynamics , 2019, IEEE Transactions on Automatic Control.

[18]  Ju H. Park,et al.  Dissipative Fuzzy Tracking Control for Nonlinear Networked Systems With Quantization , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[19]  Xingbao Gao,et al.  Stability and synchronization control of inertial neural networks with mixed delays , 2020, Appl. Math. Comput..

[20]  Ting Li,et al.  A new approach to fast global finite-time stabilization of high-order nonlinear system , 2017, Autom..

[21]  Changchun Hua,et al.  Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control , 2019, Appl. Math. Comput..

[22]  Françoise Lamnabhi-Lagarrigue,et al.  Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control , 2016, Autom..

[23]  Iasson Karafyllis,et al.  Sampled-Data Stabilization of Nonlinear Delay Systems with a Compact Absorbing Set , 2016, SIAM J. Control. Optim..

[24]  Dorothée Normand-Cyrot,et al.  Further results on sampled-data stabilization of time-delay systems , 2017 .

[25]  Dean Zhao,et al.  Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint , 2019, Appl. Math. Comput..

[26]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[27]  Dorothée Normand-Cyrot,et al.  Sampled-Data Stabilization of Nonlinear Dynamics With Input Delays Through Immersion and Invariance , 2017, IEEE Transactions on Automatic Control.

[28]  Eduardo Sontag,et al.  Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations , 1999 .

[29]  Yan Lin,et al.  Global stabilization of high-order nonlinear time-delay systems by state feedback , 2014, Syst. Control. Lett..

[30]  Dragan Nesic,et al.  Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model , 2006, Autom..

[31]  Jinde Cao,et al.  Reliable Event-Triggered Asynchronous Extended Passive Control for Semi-Markov Jump Fuzzy Systems and Its Application , 2020, IEEE Transactions on Fuzzy Systems.

[32]  Wei Lin,et al.  Robust regulation of a chain of power integrators perturbed by a lower‐triangular vector field , 2000 .

[33]  Miroslav Krstic,et al.  On compensating long actuator delays in nonlinear control , 2008, 2008 American Control Conference.

[34]  Salvatore Monaco,et al.  Advanced tools for nonlinear sampled-data systems' analysis and control , 2007, 2007 European Control Conference (ECC).

[35]  Giovanni Mattei,et al.  Multi-rate sampled-data stabilization of a class of nonlinear systems , 2015, 2015 European Control Conference (ECC).

[36]  B.D.O. Anderson,et al.  Controller design: moving from theory to practice , 1993, IEEE Control Systems.

[37]  Chunjiang Qian,et al.  Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers , 2017 .

[38]  Chunjiang Qian,et al.  Global stabilization of inherently non-linear systems using continuously differentiable controllers , 2014 .

[39]  Mrdjan Jankovic,et al.  Cross-Term Forwarding for Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

[40]  S. Monaco,et al.  Zero dynamics of sampled nonlinear systems , 1988 .

[41]  Stefano Di Gennaro,et al.  Stability analisys for a class of sampled nonlinear systems with time-delay , 2010, 49th IEEE Conference on Decision and Control (CDC).

[42]  Qing-Long Han,et al.  Networked control systems: a survey of trends and techniques , 2020, IEEE/CAA Journal of Automatica Sinica.

[43]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[44]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[45]  Wolfgang Gröbner,et al.  Contributions to the method of Lie series , 1967 .

[46]  Salvatore Monaco,et al.  Sampled-Data Stabilization; A PBC Approach , 2011, IEEE Transactions on Automatic Control.

[47]  Shengyuan Xu,et al.  Sampled-data controller design and stability analysis for nonlinear systems with input saturation and disturbances , 2019, Appl. Math. Comput..

[48]  S. Monaco,et al.  Multirate Sampling and Zero Dynamics: from linear to nonlinear , 1991 .

[49]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.