基于李雅普诺夫方程的预定时间稳定控制方法

Predefined-time stability control method based on Lyapunov function

针对固定时间稳定性存在收敛时间估计不准确且难以调整的问题,提出一种基于非负李雅普诺夫方程的全局预定时间稳定性定理.首先,改进传统固定时间稳定系统,在系统中加入一个常数项与一个指数项,以提高系统的收敛速度;然后,加入一个可调节的参数并建立其与系统收敛时间估计之间的直接关系,给出调节参数设计的显式条件,使得调节系统收敛时间更加方便、快捷.在此基础上,针对同一类非线性系统,在初始值已知的条件下,证明其也可以实现收敛时间可调节的有限时间稳定和更加准确的系统收敛时间估计.最后,对所提方法进行数值模拟验证,结果表明:所提的预定时间稳定方法可保证一类非线性系统的收敛时间是可控和可预设的.

Aiming at the problem of inaccurate estimation of the convergence time in fixed-time stability and difficulty in adjustment,a global predefined-time stability theorem based on non-negative Lyapunov function was proposed.First,the traditional fixed-time stable system was improved by adding a constant term and an exponential term to improve the convergence rate of the system.Then,an adjustable parameter was added,and a direct relationship between it and the estimation of system convergence time was established.Explicit conditions for designing the adjustment parameter were given,making the convergence time of the system more convenient and faster to adjust.On this basis,for the same class of nonlinear system,it was proved that under the condition of known initial values,a finite-time stability with adjustable convergence time and a more accurate convergence time estimation could be also achieved.Finally,numerical simulation was carried out to verify the proposed method.Results show that the proposed predefined-time stability method can guarantee that the convergence time of a class of nonlinear systems is controllable and presettable.