受正弦扰动时滞非线性系统的近似最优减振控制

Approximate optimal damping control for time-delay nonlinear systems with sinusoidal disturbances

研究时滞非线性系统在正弦扰动作用下的最优减振控制问题,给出一种无时滞近似最优减振控制律的迭代方法.通过假设Lagrange算子,将由原系统最优控制问题得到的既含时滞项又含有超前项的非线性两点边值问题转换为新的有利于求解的形式,再通过构造序列将其转化为不含时滞项和超前项的线性非齐次两点边值问题序列.证明了该序列的收敛性.通过交替迭代序列得到了系统最优减振控制律.仿真结果表明,该方法在不同时滞下对扰动都具有很好的鲁棒性.

A non-delay approximate optimal approach of solving the optimal damping control （ODC） law is presented. By supposing the Lagrange operator, an original nonlinear two-point boundary value （TPBV） problem with both timedelay and time-advance terms is transformed into new form solved conveniently, then by constructing sequences, a sequence of linear TPBV problems without delay or advance terms are obtained. The sequence of the solutions uniformly converges to the solution of the original optimal control problem. By iterative solution, the approximate ODC law is obtained. Simulation results show the approximate ODC law is robust to sinusoidal disturbances in different time-delay.