摘要
伪谱法通过全局插值多项式参数化状态和控制变量,将最优控制问题(OCP)转化为非线性规划问题(NLP)进行求解,是一类具有更高求解效率的直接法.总结Legendre伪谱法转化Bolza型最优控制问题的基本框架,推导OCP伴随变量与NLP问题KKT乘子的映射关系,建立基于拟牛顿法的LGL配点数值计算方法,并针对非光滑系统,进一步研究分段伪谱逼近策略.基于上述理论开发通用OCP求解器,并对3个典型最优控制问题进行求解,结果表明了所提出方法和求解器的有效性.
The pseudo-spectral method approximates control and state variables through global interpolation polynomials, then discrete the optimal control problem（OCP） to a nonlinear programming problem（NLP） effectively. It’s a kind of direct method with higher solving efficiency. The basic framework of the Legendre pseudo-spectral method converting the Bolza OCP into NLP is summarized, and the mapping between the costates of OCP and the KKT multiplier to NLP is derived. Furthermore, a numerical method is elaborated based on the quasi-Newton method in order to calculate the LGL collocation accurately. The multiphase strategy is also being introduced for non-smooth systems. Finally, a universal optimal control solver POPS（pseudo-spectral optimal control problem solver） is developed based on the Legendre pseudo-spectral method in Matlab. Three typical optimal control problems are solved by using the solver POPS, and the results show the effectiveness of the proposed method and solver POPS.
出处
《控制与决策》
EI
CSCD
北大核心
2014年第12期2113-2120,共8页
Control and Decision
基金
国家自然科学基金项目(51205228)
清华大学自主科研计划项目(2012THZ0)
关键词
最优控制
伪谱法
非线性规划
数值求解
optimal control
pseudo-spectral method
nonlinear programming
numerical implementation
