Robust control of nonlinear uncertain systems via sliding mode with backstepping design

Robust feedback control for uncertain nonlinear systems has been extensively studied. The systems we study do not belong to any of the existing stabilizable classes. Without loss of generality, we assume only that the known part of the system is feedback linearizable; and the remaining part, containing the uncertain dynamics, can be of any type and is bounded only by some cascaded functions. Our method is based on backstepping design and the sliding-mode method. This combined technique will be used to regulate a large class of systems without the need for strong assumptions. We develop a control law incorporating backstepping and sliding-mode control via system extension to stabilize uncertain systems whose uncertainties satisfy some cascaded boundary conditions. Note that the uncertainties themselves do not need to be in a cascaded form. The algorithm is given for multidimensional uncertain systems. We study a three-dimensional system as an example. Examples and simulations show that the combined control law attenuates high-frequency chattering.