Robust control of a class of non-affine nonlinear systems by state and output feedback

Abstract

Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers: the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded (UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.

Keywords

robust control / non-affine nonlinear system / uncertainty / stability

References

[1] ZhouH-b, YingH, DuanJ-an. Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems [J]. Journal of Central South University of Technology, 2011, 18: 760-766

[2] BelarbiK, ChemachemaM. Stable direct adaptive neural network controller with a fuzzy estimator of the control error for a class of perturbed nonlinear systems [J]. IEE Proc Control Theory Applications, 2007, 1(5): 1398-1404

[3] ParkJ H, KimS H, MoomC J. Adaptive neural control for strict-feedback nonlinear systems without backstepping [J]. IEEE Transactions on Neural Networks, 2009, 20(7): 1204-1209

[4] GeS S, HangC C, ZhangT. Nonlinear adaptive control using neural networks and its application to CSTR systems [J]. Journal of Process Control, 1999, 9(4): 313-323

[5] HsuC T, ChenS L. Nonlinear control of a 3-pole active magnetic bearing system [J]. Automatica, 2003, 39: 291-298

[6] ShirliaevA S, LudvigsenH, EgelandO, FradkovA L. Swinging up of non-affine in control pendulum [C]. Proc American Control Conf. San Diego, California, USA, 19994039-4044

[7] GohC J. Model reference control of nonlinear systems via implicit function emulation [J]. Int J Control, 1994, 60: 91-115

[8] GohC J, LeeT H. Direct adaptive control of nonlinear systems via implicit function emulation [J]. Control Theory and Advance Technology, 1994, 10(3): 539-552

[9] CaliseA J, HovakimyanN, IdanM. Adaptive output feedback control of nonlinear systems using neural networks [J]. Automatica, 2001, 37: 1201-1211

[10] HovakimyanN, NardiF, CaliseA J. A novel error observer-based adaptive output feedback approach for control of uncertain systems [J]. IEEE Trans Automatic Control, 2002, 47(8): 1310-1314

[11] ParkJ H, KimS H. Direct adaptive output-feedback fuzzy controller for a nonaffine nonlinear system [J]. IEE Proc Control Theory Applications, 2004, 51(1): 65-72

[12] ParkJ H, HuhS H, KimS H, SeoS J, ParkG T. Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks [J]. IEEE Transactions on Neural Networks, 2005, 16(2): 414-422

[13] GeS S, HangC C, ZhangT. Adaptive neural network control of nonlinear systems by state and output feedback [J]. IEEE Trans Syst Man and Cybernetics B Cybernetics, 1999, 29(6): 818-828

[14] GeS S, WangC. Adaptive NN control of uncertain nonlinear pure-feedback systems [J]. Automatica, 2002, 38: 671-682

[15] WangC, HillD J, GeS S, ChenG. An ISS-modular approach for adaptive neural control of pure-feedback systems [J]. Automatica, 2006, 42: 723-731

[16] BehtashS. Robust output tracking for nonlinear system [J]. Int J Control, 1990, 51(6): 1381-1407