Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. A novel Lyapunov-Krasovskii functional is employed to compensate for the unknown function of current delayed state, which is effectively free from any restrictive assumption on unknown time-delay functions. The proposed control scheme guarantees the boundedness of all the signals in the closed-loop system and the tracking performance. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.