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.
FerraraAGiacominiL (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 Control122(1): 33–39.
8.
GeSSWangC (2002) Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica38(4): 671–682.
9.
HuJZhangH (2013) Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles. Automatica49(7): 2160–2167.
10.
IsidoriA (1999) Nonlinear Control Systems II. London: Springer.
11.
LiHWuLGaoH. (2012) Reference output tracking control for a flexible air-breathing hypersonic vehicle via output feedback. Optimal Control Applications and Methods33(4): 461–487.
12.
LiH-YHuY-ARenJ-C. (2012) Dynamic feedback backstepping control for a class of MIMO nonaffine block nonlinear systems. Mathematical Problems in Engineering, 1–18.
13.
LinWQianCJ (2002) Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Transaction on Automatic Control47(8): 1249–1266.
14.
LiuXLinZ (2012) On the backstepping design procedure for multiple input nonlinear systems. International Journal of Robust and Nonlinear Control22(8): 918–932.
15.
ParkJYParkGT (2003) Robust adaptive fuzzy controller for nonaffine nonlinear systems with dynamic rule activation. International Journal of Robust and Nonlinear Control13(2): 117–139.
16.
RenCTongSLiY (2012) Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties. Nonlinear Dynamics67(2): 941–955.
17.
SharmaMCaliseAJ (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.
SwaroopDHedrickJKYipPP. (2000) Dynamic surface control for a class of nonlinear systems. IEEE Transactions on Automatic Control45(10): 1893–1899.
19.
TongSLiuCLiY (2012) Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain. Neurocomputing77(1): 58–70.
20.
WangCHillDJGeSS. (2006) An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica42(5): 723–731.
21.
WangD (2011) Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. International Journal of Robust and Nonlinear Control21(5): 527–541.
22.
WangDHuangJ (2002) Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form. Automatica38(8): 1365–1372.
23.
YanHJiH (2012) Integrated guidance and control for dual-control missiles based on small-gain theorem. Automatica48(10): 2686–2692.
24.
ZhangTPGeSS (2008) Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica44(7): 1895–1903.
25.
ZhaoQLinY (2012) Adaptive dynamic surface control for pure-feedback systems. International Journal of Robust and Nonlinear Control22(14): 1647–1660.
26.
ZongQJiYWangF (2012) Input-to-state stability-modular command filtered back-stepping control of strict-feedback systems. IET Control Theory and Applications6(8): 1125–1129.
