Adaptive neural novel prescribed performance control for non-affine pure-feedback systems with input saturation
An error constraint control problem is considered for pure-feedback systems with non-affine functions being possibly in-differentiable. A new constraint variable is used to construct virtual control that guarantees the tracking error within the transient and steady-state performance envelopment. The new error transformation avoids non-differentiable problems and complex deductions caused by traditional error constraint approaches. A locally semi-bounded and continuous condition for non-affine functions is employed to ensure the controllability and transform the closed-loop system into a pseudo-affine form. An auxiliary system with bounded compensation term is proposed for nonlinear systems with input saturation. On the basis of backstepping technique, an adaptive neural controller is designed to handle unknown terms and circumvent repeated differentiations of virtual controls. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory. Asymptotic tracking is achieved without violating control input constraint and error constraint. Two examples are performed to verify the theoretical findings.
KeywordsNon-affine Input saturation Adaptive neural control Prescribed performance
The authors would like to express their sincere thanks to anonymous reviewers for their helpful suggestions for improving the technical note.
This work was supported by National Natural Science Foundation of China [Grant number. 61603410 & 61573374], National Basic Research Program of China [Grant number. 2014CB744900] and Young Talent Fund of University Association for Science and Technology in Shaanxi, China [grant number. 20170107].
Compliance with ethical standards
Conflict of interest
The authors declare that there exists no conflict of interest.
- 6.Wang, C., Wu, Y., Yu, J.: Barrier Lyapunov functions-based adaptive control for nonlinear pure-feedback systems with time-varying full state constraints. Int. J. Control Autom. Syst. 15(16), 1–9 (2017)Google Scholar
- 8.Hackl, C.M., Ji, Y., Schroder, D.: Enhanced funnel-control with improved performance. IEEE Conf. Control Autom. 115(1), 1–6 (2007)Google Scholar
- 24.Bechlioulis C.P., Kyriakopoulos K.J.: Robust model-free formation control with prescribed performance for nonlinear multi-agent systems. In: IEEE International Conference on Robotics and Automation, pp 1268–1273 (2015)Google Scholar
- 32.Marantos, P., Bechlioulis, C.P., Kyriakopoulos, K.J.: Robust trajectory tracking control for small-scale unmanned helicopters with model uncertainties. IEEE Trans. Control Syst. 99, 1–12 (2017)Google Scholar
- 33.Liu, Y.J., Tong, S.: Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead zone. IEEE Trans. Fuzzy Syst. 23(5), 1341–1347 (2015)Google Scholar
- 45.Zhang, Z., Duan, G., Hou, M.: Global finite time stabilization of pure-feedback systems with input dead zone nonlinearity. J. Frankl. I. (2017). doi: 10.1016/j.jfranklin.2017.12.040.Google Scholar
- 59.Hartman, E.J., Keeler, J.D., Kowalski, J.M.: Layered neural networks with Gaussian hidden units as universal approximations. Neurocomputing 2(2), 210–215 (1990)Google Scholar
- 60.Park, J., Sandberg, L.W.: Universal approximation using radial-basis-function networks. Neurocomputing 3(2), 246–257 (1990)Google Scholar