Adaptive Finite-Time Control for a Class of p-Normal Nonlinear Systems

Compared with asymptotic stability or exponential stability, finite-time stability has the advantages of fast convergence, high tracking accuracy, and strong robustness. Therefore, finite-time control problem has received extensive attention. An adaptive finite-time control problem is discussed in this brief for a class of $p$ -normal nonlinear systems. First, an observer-based state feedback controller is constructed such that the nominal system is globally finite-time stable. Then, the nonlinear terms are dominated by introducing a dynamic gain. Based on Lyapunov stability theory, it is proved that the system state converges to origin in a finite time and the dynamic gain is bounded. Finally, an example is used to illustrate the effectiveness of the proposed control strategy.