Fuzzy Echo State Neural Networks and Funnel Dynamic Surface Control for Prescribed Performance of a Nonlinear Dynamic System

This paper presents a funnel dynamic surface control combined with fuzzy echo state networks (FESNs) for the prescribed tracking performance of a strict feedback multi-input-multi-output (MIMO) nonlinear dynamic system. A new funnel variable is defined so that the funnel virtual control forces the tracking error to fall within funnel boundary, and adaptive FESN method is also proposed to improve the approximation performance in conventional neural network algorithms. A strict feedback controller and adaptive laws for estimating the uncertainties were derived using the recursive steps of dynamic surface control based on the Lyapunov stability theory. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The performance of the proposed control scheme was validated by simulations and experimental applications to the tracking control of a MIMO nonlinear system and a robot manipulator.

[1]  Wei Wang,et al.  Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance , 2010, Autom..

[2]  Yuichi Nakamura,et al.  Approximation of dynamical systems by continuous time recurrent neural networks , 1993, Neural Networks.

[3]  D. Mayne Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[4]  Christian Endisch,et al.  Contributions to non-identifier based adaptive control in mechatronics , 2009, Robotics Auton. Syst..

[5]  Eugene P. Ryan,et al.  Tracking control with prescribed transient behaviour for systems of known relative degree , 2006, Syst. Control. Lett..

[6]  Stefan Preitl,et al.  Fuzzy Control Systems With Reduced Parametric Sensitivity Based on Simulated Annealing , 2012, IEEE Transactions on Industrial Electronics.

[7]  Charalampos P. Bechlioulis,et al.  Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems , 2009, Autom..

[8]  Shengyuan Xu,et al.  Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[10]  Mei Su,et al.  Indirect Four-Leg Matrix Converter Based on Robust Adaptive Back-Stepping Control , 2011, IEEE Transactions on Industrial Electronics.

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

[12]  P. P. Yip,et al.  Multiple Sliding Surface Control: Theory and Application , 2000 .

[13]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[14]  Zi-Jiang Yang,et al.  Robust Output Feedback Control of a Class of Nonlinear Systems Using a Disturbance Observer , 2011, IEEE Transactions on Control Systems Technology.

[15]  Charalampos P. Bechlioulis,et al.  Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance , 2008, IEEE Transactions on Automatic Control.

[16]  Shengyuan Xu,et al.  Adaptive Output-Feedback Fuzzy Tracking Control for a Class of Nonlinear Systems , 2011, IEEE Transactions on Fuzzy Systems.

[17]  Herbert Jaeger,et al.  Optimization and applications of echo state networks with leaky- integrator neurons , 2007, Neural Networks.

[18]  Charalampos P. Bechlioulis,et al.  Prescribed Performance Adaptive Control for Multi-Input Multi-Output Affine in the Control Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

[19]  Shuzhi Sam Ge,et al.  Control of Coupled Vessel, Crane, Cable, and Payload Dynamics for Subsea Installation Operations , 2011, IEEE Transactions on Control Systems Technology.

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

[21]  Han-Pang Huang,et al.  Development and Fuzzy Control of a Pipe Inspection Robot , 2010, IEEE Transactions on Industrial Electronics.

[22]  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.

[23]  Jun Zhao,et al.  Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function , 2013, Int. J. Syst. Sci..

[24]  Eugene P. Ryan,et al.  Tracking with Prescribed Transient Behavior for Nonlinear Systems of Known Relative Degree , 2007, SIAM J. Control. Optim..

[25]  Long Cheng,et al.  Adaptive neural network tracking control of robot manipulators with prescribed performance , 2011 .

[26]  Herbert Jaeger,et al.  The''echo state''approach to analysing and training recurrent neural networks , 2001 .

[27]  Milos Manic,et al.  Fuzzy Force-Feedback Augmentation for Manual Control of Multirobot System , 2011, IEEE Transactions on Industrial Electronics.

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

[29]  Christoph M. Hackl,et al.  High-gain adaptive position control , 2011, Int. J. Control.

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

[31]  Charalampos P. Bechlioulis,et al.  Neuro-Adaptive Force/Position Control With Prescribed Performance and Guaranteed Contact Maintenance , 2010, IEEE Transactions on Neural Networks.

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

[33]  Kwang Y. Lee,et al.  Diagonal recurrent neural networks for dynamic systems control , 1995, IEEE Trans. Neural Networks.

[34]  Jing Peng,et al.  An Efficient Gradient-Based Algorithm for On-Line Training of Recurrent Network Trajectories , 1990, Neural Computation.

[35]  Charalampos P. Bechlioulis,et al.  Robust Partial-State Feedback Prescribed Performance Control of Cascade Systems With Unknown Nonlinearities , 2011, IEEE Transactions on Automatic Control.

[36]  Hans Schuster,et al.  PI-Funnel Control for Two Mass Systems , 2009, IEEE Transactions on Automatic Control.