非线性相似组合大系统最优控制的逐次逼近过程

研究一类仿射非线性相似组合大系统关于二次型性能指标的最优控制问题．首先通过模型简化，将非线性相似组合大系统化为若干个准解耦的子系统；然后利用非线性系统最优控制的逐次逼近设计方法，将求解高阶强耦合的非线性两点边值问题简化为求解一族解耦的线性两点边值问题序列．该线性两点边值问题序列的解一致收敛于非线性相似组合大系统的最优控制，得到的最优控制律由线性最优控制的解析项与非线性补偿序列的极限项组成．通过截取最优控制非线性补偿序列的有限次逼近值．得到了非线性组合大系统的次优控制律．

Successive approximation procedure of optimal control for nonlinear similar composite systems

The optimal control problem for a class of affine nonlinear large-scale systems with similar composite structure is considered. The nonlinear large-scale system is first transformed into some quasi-decoupling subsystems by using the modeling technique. Then the high order, strongly coupled, nonlinear two-point boundary value problem is transformed into a sequence of linear decoupling two-point boundary value (TPBV) problems through a successive approximation procedure. The solution sequence of the TPBV problems uniformly converges to the optimal control for the original problem. The optimal control law obtained consists of an accurate linear term and a nonlinear compensating sequence. A suboptimal control law is obtained by using a finite iterative result of the nonlinear compensating sequence.