Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

ABSTRACT In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

[1]  Ho-Lim Choi,et al.  Non-predictor controller for feedforward and non-feedforward nonlinear systems with an unknown time-varying delay in the input , 2016, Autom..

[2]  Salim Ibrir,et al.  Adaptive observers for time-delay nonlinear systems in triangular form , 2009, Autom..

[3]  Jianbin Qiu,et al.  Adaptive Fuzzy Backstepping Control for A Class of Nonlinear Systems With Sampled and Delayed Measurements , 2015, IEEE Transactions on Fuzzy Systems.

[4]  Xudong Ye,et al.  Adaptive stabilization of time-delay feedforward nonlinear systems , 2011, Autom..

[5]  Yong Zhang,et al.  Weighted Fuzzy Observer-Based Fault Detection Approach for Discrete-Time Nonlinear Systems via Piecewise-Fuzzy Lyapunov Functions , 2016, IEEE Transactions on Fuzzy Systems.

[6]  Ho-Lim Choi,et al.  Non-predictor control of a class of feedforward nonlinear systems with unknown time-varying delays , 2016, Int. J. Control.

[7]  Prashanth Krishnamurthy,et al.  Generalized State Scaling and Applications to Feedback, Feedforward, and Nontriangular Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[8]  Hamid Reza Karimi,et al.  Reliable Output Feedback Control of Discrete-Time Fuzzy Affine Systems With Actuator Faults , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Reza Olfati-Saber,et al.  Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles , 2001 .

[10]  Gang Feng,et al.  Robust stabilisation for a class of time-delay systems with triangular structure , 2007 .

[11]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .

[12]  Shihua Li,et al.  Global Stabilization of a Class of Feedforward Systems with Lower-Order Nonlinearities , 2010, IEEE Transactions on Automatic Control.

[13]  Ho-Lim Choi,et al.  Regulation of lower triangular and non‐triangular nonlinear systems with uncertain high‐order nonlinearities via dynamic gain control , 2017 .

[14]  Jianhong Wu,et al.  Introduction to Functional Differential Equations , 2013 .

[15]  Wei Lin,et al.  Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach , 2007, Syst. Control. Lett..

[16]  Wim Michiels,et al.  The Effect of Approximating Distributed Delay Control Laws on Stability , 2004 .

[17]  Jong-Tae Lim,et al.  Global regulation of a class of feedforward and non-feedforward nonlinear systems with a delay in the input , 2012, Autom..

[18]  M. Golicnik,et al.  Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model. , 2010, Analytical biochemistry.

[19]  Salim Ibrir.  Observer-based control of a class of time-delay nonlinear systems having triangular structure , 2011, Autom..

[20]  Ho-Lim Choi,et al.  Output feedback regulation of a chain of integrators with unknown time-varying delays in states and input , 2015, Autom..

[21]  Jong-Tae Lim,et al.  Asymptotic stabilization of an input-delayed chain of integrators with nonlinearity , 2010, Syst. Control. Lett..

[22]  Jianbin Qiu,et al.  Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay , 2015 .

[23]  Wei Lin,et al.  Robust control of uncertain systems with polynomial nonlinearity by output feedback , 2009 .

[24]  Kemei Zhang,et al.  Output feedback stabilisation of high-order nonlinear feedforward time-delay systems , 2017, Int. J. Syst. Sci..

[25]  Laurent Praly.  Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate , 2003, IEEE Trans. Autom. Control..

[26]  Jianbin Qiu,et al.  Fuzzy-Model-Based Reliable Static Output Feedback $\mathscr{H}_{\infty }$ Control of Nonlinear Hyperbolic PDE Systems , 2016, IEEE Transactions on Fuzzy Systems.

[27]  Chenghui Zhang,et al.  Output feedback control of large-scale nonlinear time-delay systems in lower triangular form , 2013, Autom..

[28]  Jianbin Qiu,et al.  Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems , 2017, IEEE Transactions on Fuzzy Systems.

[29]  Jianbin Qiu,et al.  Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T–S Fuzzy Observer-Based Implementation , 2017, IEEE Transactions on Cybernetics.

[30]  Jong-Tae Lim,et al.  Stabilisation of non-linear systems with unknown growth rate by adaptive output feedback , 2010, Int. J. Syst. Sci..

[31]  Jianbin Qiu,et al.  Adaptive Neural Control of Stochastic Nonlinear Time-Delay Systems With Multiple Constraints , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.