Approximation-based adaptive control of uncertain non-linear pure-feedback systems with full state constraints

This study proposes an adaptive approximation-based control approach for non-linear pure-feedback systems in the presence of full state constraints. Completely non-affine non-linear functions are considered and assumed to be unknown. The dynamic surface design based on integral barrier Lyapunov functionals is provided to achieve both the desired tracking performance and the constraints satisfaction, in consideration of the full-state-constrained non-affine non-linearities. In this design procedure, simple sufficient conditions for choosing control gains, which can be checked off-line, are established to guarantee the feasibility of the controller. The function approximation technique is employed to estimate unknown non-linearities induced from the controller design procedure where the adaptive laws using the projection operator are designed to ensure the boundedness of the function approximators in the feasibility conditions. It is shown that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while all state variables always remain in the constrained state space.

[1]  A. H. Nayfeh,et al.  Development of an analytical model of wing rock for slender delta wings , 1989 .

[2]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

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

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

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

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

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

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

[9]  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.

[10]  B. Karimi,et al.  Robust Adaptive Control of Nonaffine Nonlinear Systems Using Radial Basis Function Neural Networks , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

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

[12]  Alexander F. Vakakis,et al.  Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non‐linear energy sinks , 2006 .

[13]  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..

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

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

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

[17]  Keng Peng Tee,et al.  Control of nonlinear systems with full state constraint using a Barrier Lyapunov Function , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

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

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

[21]  Keng Peng Tee,et al.  Control of state-constrained nonlinear systems using Integral Barrier Lyapunov Functionals , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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