Backstepping control for output-constrained nonlinear systems based on nonlinear mapping

In this paper, nonlinear mapping (NM)-based backstepping control design is presented for a class of strict-feedback nonlinear systems with output constraint. By mapping output value set onto the set of all real numbers, the constrained system is transformed into a new strict-feedback unconstrained system to employ the traditional backstepping control while simultaneously preventing the constraint from being violated. It is proved that the original system has the similar convergence and bounded properties with the new one. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Furthermore, the comparison with barrier Lyapunov function-based algorithm reveals the advantages of NM algorithm. The closed-loop system is guaranteed to be stable in the sense that all signals involved remain bounded, and the tracking error converges to zero asymptotically. Simulation studies illustrate the performance of the proposed control.

[1]  Shuzhi Sam Ge,et al.  Adaptive Neural Network Control of Robotic Manipulators , 1999, World Scientific Series in Robotics and Intelligent Systems.

[2]  Jian-Xin Xu,et al.  Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties , 2013, Autom..

[3]  Yan-Jun Liu,et al.  Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems , 2007, Inf. Sci..

[4]  Fengjun Yan,et al.  Fuel-assisted in-cylinder oxygen fraction transient trajectory shaping control for diesel engine combustion mode switching , 2011, Proceedings of the 2011 American Control Conference.

[5]  Marko Bacic,et al.  Model predictive control , 2003 .

[6]  Yansheng Yang,et al.  A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  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.

[8]  A. Benaskeur,et al.  Backstepping-based adaptive PID control , 2002 .

[9]  Eduardo F. Camacho,et al.  Model predictive control in the process industry , 1995 .

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

[11]  Miroslav Krstic,et al.  Nonovershooting Control of Strict-Feedback Nonlinear Systems , 2006, IEEE Transactions on Automatic Control.

[12]  Keng Peng Tee,et al.  Adaptive Control of Electrostatic Microactuators With Bidirectional Drive , 2009, IEEE Transactions on Control Systems Technology.

[13]  John T.W. Yeow,et al.  Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking , 2012 .

[14]  Shuzhi Sam Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[16]  George A. Rovithakis,et al.  Adaptive Dynamic Output Feedback Neural Network Control of Uncertain MIMO Nonlinear Systems With Prescribed Performance , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[17]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[18]  Martin Guay,et al.  Parameter convergence in adaptive extremum-seeking control , 2007, Autom..

[19]  S. Jain,et al.  Decentralized adaptive control of a class of large-scale interconnected nonlinear systems , 1997, IEEE Trans. Autom. Control..

[20]  Jian-Xin Xu,et al.  State-Constrained Iterative Learning Control for a Class Of MIMO Systems , 2013, IEEE Transactions on Automatic Control.

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

[22]  Faa-Jeng Lin,et al.  Adaptive backstepping sliding mode control for linear induction motor drive , 2002 .

[23]  Fengjun Yan,et al.  Non-equilibrium transient trajectory shaping control via multiple Barrier Lyapunov Functions for a class of nonlinear systems , 2010, Proceedings of the 2010 American Control Conference.

[24]  Yongming Li,et al.  Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function , 2014 .

[25]  Kenji Hirata,et al.  Reference Governor for Constrained Systems with Time-varying References , 2006, 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

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

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

[28]  Junmin Li,et al.  Decentralized Output-Feedback Neural Control for Systems With Unknown Interconnections , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Guoying Liu,et al.  Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions , 2011 .

[30]  X. Guan,et al.  Dynamic surface control for a class of state-constrained non-linear systems with uncertain time delays , 2012 .

[31]  Haizhou Li,et al.  Adaptive admittance control of a robot manipulator under task space constraint , 2010, 2010 IEEE International Conference on Robotics and Automation.

[32]  Keng Peng Tee,et al.  Adaptive control for parametric output feedback systems with output constraint , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[33]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[34]  Maria Adler,et al.  Stable Adaptive Systems , 2016 .

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

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

[37]  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.