一类非匹配不确定非线性系统快速加幂积分控制

Fast adding one power integrator control for a class of nonlinear systems with mismatched uncertainties

针对传统加幂积分控制在远离原点区域收敛速度过慢的问题,基于加幂积分控制和快速有限时间Lyapunov理论对一类非匹配不确定非线性系统提出一种快速化的加幂积分控制.该方案保留加幂积分控制有限时间收敛、无抖振、无奇异性的优点,能够加快传统加幂积分控制的收敛速度,具有更强的鲁棒性、更小的稳态误差.从理论上证明了所提出方案的所有优越性,并通过仿真验证了所提出的所有结论.

Traditional adding one power integrator control（AOPIC） convergence speed is even slower than linear control if the states are far from origin. To solve this problem, based on the traditional AOPIC and fast finite time Lyapunov theorem（FFTLT）, a fast adding one power integrator control（FAOPIC） method is proposed for a class of nonlinear systems with mismatched uncertainties and external disturbance, which has the advantages of the AOPIC and FFTLT. Then it is strictly proved that the FAOPIC can speed up the convergence process of AOPIC, which is just exponential convergent or non-fast finite time convergent at any point, and it has stronger robustness and smaller steady error. Simulations are conducted to verify that the proposed method has significant better performance than AOPIC, and is very suitable for engineering application.