Global output feedback practical tracking for time-delay systems with uncertain polynomial growth rate

Abstract In this paper, the problem of global practical output tracking is investigated by output feedback for a class of uncertain nonlinear time-delay systems. Compared with the existing results, we allow the nonlinearities to nonlinearly grow in unmeasured free-delay and time-delay states with the uncertain time-delay output polynomial growth rate. Based on the ideas of universal adaptive control and dead zone, we develop an adaptive high-gain observer with a novel monotone non-decreasing dynamic law. By the Lyapunov–Krasovskii theorem, a memoryless controller is constructed to achieve global practical output tracking for uncertain nonlinear systems with multiple time delays. Finally, two examples are given to illustrate the usefulness of our results.

[1]  Wei Lin,et al.  Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization , 2003, IEEE Trans. Autom. Control..

[2]  Wei Guan,et al.  Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays , 2012, Int. J. Syst. Sci..

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

[4]  Wei Lin,et al.  Universal adaptive control of nonlinear systems with unknown growth rate by output feedback , 2006, Autom..

[5]  Shengyuan Xu,et al.  Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance , 2010 .

[6]  Yan Lin,et al.  Adaptive Control of Nonlinear Time-Delay Systems With Application to a Two-Stage Chemical Reactor , 2015, IEEE Transactions on Automatic Control.

[7]  Diederich Hinrichsen,et al.  Destabilization by output feedback , 1992, Differential and Integral Equations.

[8]  Gang Feng,et al.  Robust controller design of a class of nonlinear time delay systems via backstepping method , 2008, Autom..

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

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

[11]  Abdallah BenAbdallah,et al.  Adaptive practical output tracking control for a class of uncertain nonlinear systems , 2015, Int. J. Syst. Sci..

[12]  Junyong Zhai,et al.  Global output feedback control for a class of high-order feedforward nonlinear systems with input delay. , 2013, ISA transactions.

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

[14]  Wei Lin,et al.  Adaptive regulation of high-order lower-triangular systems : an adding a power integrator technique , 2000 .

[15]  YunGang Liu,et al.  Global Practical Tracking by Output Feedback for Nonlinear Systems with Unknown Growth Rate and Time Delay , 2011, Science China Information Sciences.

[16]  Ju H. Park,et al.  Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures , 2015 .

[17]  Yan Lin,et al.  Global adaptive output feedback control for a class of uncertain nonlinear time-delay systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[18]  Lin Chai.  Global stabilization for a class of non-linearly parametrized time-delay systems with output feedback dynamic linear controllers , 2015, IMA J. Math. Control. Inf..

[19]  Shengyuan Xu,et al.  Adaptive Output Feedback Control for Nonlinear Time-Delay Systems by Fuzzy Approximation Approach , 2013, IEEE Transactions on Fuzzy Systems.

[20]  Luc Baron,et al.  Design of Stabilizing Controllers With a Dynamic Gain for Feedforward Nonlinear Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

[21]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[22]  A. Isidori.  Nonlinear Control Systems , 1985 .

[23]  Riccardo Marino,et al.  Output Feedback Control of a Class Of Nonlinear Systems , 1992 .

[24]  Wei Lin,et al.  Practical output tracking of nonlinear systems with uncontrollable unstable linearization , 2002, IEEE Trans. Autom. Control..

[25]  Qi Gong,et al.  Global practical tracking of a class of nonlinear systems by output feedback , 2007, Autom..

[26]  Junyong Zhai,et al.  Universal adaptive regulation for a class of nonlinear systems with unknown time delays and output function via output feedback , 2013, J. Frankl. Inst..

[27]  Peter Xiaoping Liu,et al.  Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems , 2009, IEEE Transactions on Industrial Electronics.

[28]  Zhong-Ping Jiang,et al.  Linear output feedback with dynamic high gain for nonlinear systems , 2004, Syst. Control. Lett..

[29]  W. Dayawansa,et al.  Global stabilization by output feedback: examples and counterexamples , 1994 .

[30]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[31]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[32]  Junwei Lu,et al.  Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays , 2012 .

[33]  J. Zhai,et al.  Global adaptive output feedback control for a class of nonlinear time-delay systems. , 2014, ISA transactions.

[34]  YunGang Liu,et al.  Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions , 2010, SIAM J. Control. Optim..

[35]  Shengyuan Xu,et al.  Exact tracking control of nonlinear systems with time delays and dead-zone input , 2015, Autom..