Prescribed-time tracking control for nonlinear systems with linear time-varying state feedback

In this article, the prescribed-time tracking control problem is taken into consideration for a class of strict feedback single-input-single-output(SISO) systems with unknown nonlinear items. A novel 3-segment piecewise parametric function is introduced in the prescribed time. By utilising the unique positive definite solution of the parametric Lyapunov equation (PLE), a linear state feedback controller with a time-varying gain is designed to achieve prescribed-time output tracking control with the impact of unknown nonlinear terms attenuated. The existing parametric function has a disadvantage that it is not differentiable in some time spots, therefore it is modified to be differentiable and bounded during the whole time span. It is proved that with the proposed linear time-varying controller, the Lyapunov-like function is bounded, which implies that all the state signals, control signals, and the output tracking error are bounded not only before the prescribed time but also beyond the prescribed time. Finally, the simulation results and simulation comparisons on a second-order nonlinear system verify the effectiveness of the proposed control mechanism. Moreover, the proposed controller is applied to control a tower crane, which demonstrates the feasibility of the proposed method in applications.