Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

An adaptive neural network control problem of completely non-affine pure-feedback systems with a time-varying output constraint and external disturbances is investigated. For the controller design, we presents an appropriate Barrier Lyapunov Function (BLF) considering both the time-varying output constraint and the control direction nonlinearities induced from the implicit function theorem and mean value theorem. From an error transformation, the BLF dependent on the time-varying constraint is transformed into the explicitly time-independent BLF. Based on the explicitly time-independent BLF, an adaptive dynamic surface control scheme using the function approximation technique is designed to ensure both the constraint satisfaction and the desired tracking ability. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin while the time-varying output constraint is never violated.

[1]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

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

[3]  Tao Zhang,et al.  Stable Adaptive Neural Network Control , 2001, The Springer International Series on Asian Studies in Computer and Information Science.

[4]  I. Cock.  Encyclopedia of Life Support Systems (EOLSS) , 2011 .

[5]  Keng Peng Tee,et al.  Control of nonlinear systems with partial state constraints using a barrier Lyapunov function , 2011, Int. J. Control.

[6]  Philip M. Morse,et al.  Methods of Mathematical Physics , 1947, The Mathematical Gazette.

[7]  Keng Peng Tee,et al.  Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function , 2010, IEEE Transactions on Neural Networks.

[8]  Shuzhi Sam Ge,et al.  An ISS-modular approach for adaptive neural control of pure-feedback systems , 2006, Autom..

[9]  Keng Peng Tee,et al.  Control of nonlinear systems with time-varying output constraints , 2009, 2009 IEEE International Conference on Control and Automation.

[10]  Petros A. Ioannou,et al.  Adaptive Systems with Reduced Models , 1983 .

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

[12]  Frank Allgöwer,et al.  Nonlinear Model Predictive Control , 2007 .

[13]  Shuzhi Sam Ge,et al.  Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form , 2008, Autom..

[14]  Chih-Hong Lin,et al.  Robust H∞ controller design with recurrent neural network for linear synchronous motor drive , 2003, IEEE Trans. Ind. Electron..

[15]  L. Grüne,et al.  Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition , 2011 .

[16]  Gang Sun,et al.  A DSC approach to adaptive neural network tracking control for pure-feedback nonlinear systems , 2013, Appl. Math. Comput..

[17]  Ilya V. Kolmanovsky,et al.  Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor , 2002, Autom..

[18]  Qing Zhu,et al.  Adaptive Fuzzy Control of Nonlinear Systems in Pure Feedback Form Based on Input-to-State Stability , 2010, IEEE Transactions on Fuzzy Systems.

[19]  Shuzhi Sam Ge,et al.  Adaptive NN control of uncertain nonlinear pure-feedback systems , 2002, Autom..

[20]  R. Mahony,et al.  Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  Jang-Myung Lee,et al.  Adaptive fuzzy backstepping dynamic surface control for output-constrained non-smooth nonlinear dynamic system , 2012 .

[22]  Dan Wang,et al.  Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form , 2002, Autom..

[23]  Jin Bae Park,et al.  Indirect adaptive control of nonlinear dynamic systems using self recurrent wavelet neural networks via adaptive learning rates , 2007, Inf. Sci..

[24]  X. Liu,et al.  Adaptive Neural Control of Pure-Feedback Nonlinear Time-Delay Systems via Dynamic Surface Technique , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Swaroop Darbha,et al.  Dynamic surface control for a class of nonlinear systems , 2000, IEEE Trans. Autom. Control..

[26]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .

[27]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .