带持续扰动线性时滞大系统前馈反馈最优控制

Feedforward and feedback optimal control for linear large-scale systems with state time-delay affected by persistent disturbances

针对在外部持续扰动下的线性时滞大系统,提出了一种前馈反馈最优控制的逐次逼近算法;将既含有时滞项和超前项,又含有耦合项的两点边值问题,转化为既不含有时滞项和超前项,又不含有耦合项的非奇次线性两点边值问题族,该线性两点边值问题族的解序列一致收敛于原最优控制问题的解;得到的最优控制律由解析的无时滞前馈反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成,补偿项由逐次逼近法求解一族线性伴随向量方程的解序列求得;截取时滞补偿序列的有限项,得到大系统的前馈反馈最优控制律。

This paper develops a successive approximation algorithm of feedforward and feedback optimal control for linear large-scale systems with state time-delay affected by persistent disturbances. The linear two-point boundary value （TPBV） problem with time-delay terms, time-advance terms and coupling terms is transformed to a sequence of nonhomogeneous linear TPBV problems without time-delay terms, time-advance terms and coupling terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original problem. The optimal control law obtained is composed of feedforward and feedback optimal terms without time -delay in analytic forms and a compensation term with time-delay in a sequence limit form of adjoint vectors. The compensation term can be obtained from a recursion formula of adjoint vectors. By taking the finite-times iteration of the compensation sequence, the author obtains a suboptimal control law.