Adaptive finite-time neural control of non-strict feedback systems subject to output constraint, unknown control direction, and input nonlinearities

Abstract This paper addresses the finite-time controller design for a class of nonlinear systems in the non-strict feedback form subject to unknown system dynamics and disturbances, arbitrary asymmetric time-varying output constraints, four types of input nonlinearities, and unknown control direction. Utilizing the barrier Lyapunov function (BLF) and backstepping technique, an adaptive finite-time controller has been proposed. The difficulties associating with non-strict feedback systems have been handled using the variable separation approach. Furthermore, the unknown control direction problem has been tackled by using the Nussbaum gain function. A unified framework has been utilized for handling four types of input nonlinearities, including saturation, deadzone, backlash, and hysteresis. By applying intelligent approximators, not only the unknown functions have been estimated, but also the explosion of complexity problem occurring in the backstepping technique has been avoided. To reduce the computational burden, only one adaptive law has been applied and the approximator functions are not involved in the control implementation. Under the designed controller, all closed-loop signals remain semi-globally practically finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of the origin in a finite-time. The effectiveness of the proposed controller has been demonstrated through a simulation example.