ISPS-modular command-filtered adaptive back-stepping control of non-linearly parameterized pure-feedback systems

Abstract

An input-to-state practically stable (ISPS)-modular command-filtered adaptive back-stepping control (CFABC) is investigated for non-linearly parameterized pure-feedback systems, which can obviate the complicate analytic derivatives in traditional back-stepping design. In the proposed CFABC scheme, sliding-mode-based integral filters are introduced to approximate the virtual control derivatives, to solve the ‘circular construction problem’ and the problem of an ‘explosion of complexity’ in a pure-feedback system. The resulting closed-loop system consists of a controller-filter pair, which satisfies the ISPS property, providing the celebrated small-gain theorem can be exploited to guarantee the stability of the closed-loop system. Referring to the issue of non-linearly parameterized uncertainty, adaptive laws are derived via the parameter separation technique. Numerical simulations are included to illustrate the effectiveness of the proposed control scheme.

Keywords

Algorithmic complexity control control systems design non-linear systems parametric uncertainty

Get full access to this article

View all access options for this article.

References

Abdessameud

Tayebi

(2010) Global trajectory tracking control of VTOL-UAVs without linear velocity measurements. Automatica 46(6): 1053–1059.

Astrom

Kumar

(2014) Control: a perspective. Automatica 50(1): 3–43.

Dong

Farrell

Polycarpou

. (2010) Command filtered adaptive backstepping. In: Proceedings of American Control Conference, Baltimore, MD, pp. 105–110.

Dong

Chen

(1997) Adaptive control of the uncertain Duffing oscillator. International Journal of Bifurcation and Chaos 7(7): 1651–1658.

Farrell

Polycarpou

Sharma

. (2008) Command filtered backstepping. Proceedings of American Control Conference, Seattle, WA, pp. 1923–1928.

Farrell

Polycarpou

Sharma

. (2009) Command filtered backstepping. IEEE Transactions on Automatic Control 54(6): 1391–1395.

Ferrara

Giacomini

(2000) Control of a class of mechanical systems with uncertainties via a constructive adaptive second order VSC approach. Transactions of ASME, Journal of Dynamic Systems, Measurement and Control 122(1): 33–39.

Wang

(2002) Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38(4): 671–682.

Zhang

(2013) Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles. Automatica 49(7): 2160–2167.

10.

Isidori

(1999) Nonlinear Control Systems II. London: Springer.

11.

Gao

. (2012) Reference output tracking control for a flexible air-breathing hypersonic vehicle via output feedback. Optimal Control Applications and Methods 33(4): 461–487.

12.

H-Y

Y-A

Ren

J-C

. (2012) Dynamic feedback backstepping control for a class of MIMO nonaffine block nonlinear systems. Mathematical Problems in Engineering, 1–18.

13.

Lin

Qian

(2002) Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Transaction on Automatic Control 47(8): 1249–1266.

14.

Liu

Lin

(2012) On the backstepping design procedure for multiple input nonlinear systems. International Journal of Robust and Nonlinear Control 22(8): 918–932.

15.

Park

(2003) Robust adaptive fuzzy controller for nonaffine nonlinear systems with dynamic rule activation. International Journal of Robust and Nonlinear Control 13(2): 117–139.

16.

Ren

Tong

(2012) Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties. Nonlinear Dynamics 67(2): 941–955.

17.

Sharma

Calise

(2002) Adaptive backstepping control for a class of nonlinear systems via multilayered neural networks. Proceedings of American Control Conference, Anchorage, AK, pp. 2683–2688.

18.

Swaroop

Hedrick

Yip

. (2000) Dynamic surface control for a class of nonlinear systems. IEEE Transactions on Automatic Control 45(10): 1893–1899.

19.

Tong

Liu

(2012) Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain. Neurocomputing 77(1): 58–70.

20.

Wang

Hill

. (2006) An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42(5): 723–731.

21.

Wang

(2011) Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. International Journal of Robust and Nonlinear Control 21(5): 527–541.

22.

Wang

Huang

(2002) Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form. Automatica 38(8): 1365–1372.

23.

Yan

(2012) Integrated guidance and control for dual-control missiles based on small-gain theorem. Automatica 48(10): 2686–2692.

24.

Zhang

(2008) Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7): 1895–1903.

25.

Zhao

Lin

(2012) Adaptive dynamic surface control for pure-feedback systems. International Journal of Robust and Nonlinear Control 22(14): 1647–1660.

26.

Zong

Wang

(2012) Input-to-state stability-modular command filtered back-stepping control of strict-feedback systems. IET Control Theory and Applications 6(8): 1125–1129.