Finite-time tracking control for time-delayed pure-feedback systems with guaranteed performance

This article investigates the finite-time tracking control problem with guaranteed performance for a class of nonlinear pure-feedback systems subject to both time-varying state delays and control input delays. Both the state delays and control input delays are assumed to be unknown yet bounded by some known constants. A new performance function is introduced that ensures the finite-time convergence of tracking errors and guaranteed performance. The key to handling both the states and input delays lies in a novel construction of the Lyapunov-Krasovskii (LK) function, which also avoids the reconstruction of the LK function in stability analysis. In addition, a continuous package function is introduced, which allows the unknown nonlinear terms arising from the uncertain perturbation and the derivation of the LK function to be eliminated. Under the proposed method, the semi-global uniform ultimate boundedness of all signals in the closed-loop system can also be ensured. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this article.