摘要
针对外部持续扰动下的线性时滞系统,提出一种前馈-反馈最优控制的逐次逼近算法.利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题族,并证明了线性两点边值问题族的解序列一致收敛于原系统最优控制律.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.通过截取时滞补偿序列的有限项,得到系统的前馈-反馈次优控制律.仿真示例表明,该方法对外部持续扰动具有良好的鲁棒性.
A successive approximation algorithm of feedforward and feedback optimal control for linear systems with state time-delay affected by persistent disturbances is presented. The linear two-point boundary value (TPBV) problem with both time-delay terms and time-advance terms is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay terms and time-advance terms. The sequence of the solutions uniformly converges to the optimal control law for the systems. 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. By taking the finite-times iteration of the compensation sequence, a suboptimal control law is obtained. Simulations show that the algorithm is robust with respect to external persistent disturbances.
出处
《控制与决策》
EI
CSCD
北大核心
2005年第5期505-510,515,共7页
Control and Decision
基金
国家自然科学基金项目(60074001)
山东省自然科学基金项目(Y2000G02).
关键词
时滞系统
逐次逼近法
最优控制
前馈一反馈控制
持续扰动
Computer simulation
Delay control systems
Feedback control
Matrix algebra
Riccati equations
Robustness (control systems)
