Finite- and Fixed-Time Learning Control for Continuous-Time Nonlinear Systems

Finite- and fixed-time parameter estimation and adaptive control have been extensively investigated in recent years. This study proposes a finite- and fixed-time learning control framework to achieve simultaneous finite/fixed-time parameter estimation and control. The proposed learning control method first estimates unknown parameters and then uses these estimates to improve the control performance. Therefore, we first consider the convergence condition of finite/fixed-time parameter estimation. Next, a novel learning-based finite/fixed control law is designed. Unlike most existing adaptation laws, the estimate is updated to improve the understanding of the system rather than eliminate the influence of uncertainties. The finite/fixed-time convergence of the system states is analyzed using a direct dynamic analysis method that differs from the long-used Lyapunov method. We show that the proposed control input satisfies the excitation condition of the finite/fixed-time estimation, indicating simultaneous estimation and control. Finally, numerical simulations are performed to verify the theoretical results.