【作者】 张倩； 吕露； 苏建忠； 王文海； 袁健全； 张泽银； 张正辉； 刘兴高；

【Author】 Qian Zhang;Lu Lv;Jianzhong Su;Wenhai Wang;Jianquan Yuan;Zeyin Zhang;Zhenghui Zhang;Xinggao Liu;State Key Laboratory of Industrial Control Technology,Control Department,Zhejiang University;Tianjin Jinhang Institute of Technical Physics;Science and Technology on Complex System Control and Intelligent Agent Cooperative Laboratory;Mathematics Department,Zhejiang University;

【机构】 浙江大学NGICS大平台工业控制技术国家重点实验室浙江大学控制学院； 天津津航技术物理研究所； 复杂系统控制与智能协同技术重点实验室； 浙江大学数学科学学院；

【摘要】 目前国内外涉及正交配置法的研究中,控制变量和状态变量均是通过Lagrange插值多项式近似,插值节点通常采用Legendre正交多项式的零点,无法利用状态变量的导数信息。考虑到最优控制问题中往往涉及状态变量的微分方程,为充分利用状态变量的导数信息,减少问题的求解规模,本文提出一种基于Hermite插值的正交配置法,通过Hermite插值多项式近似状态变量,并以Jacobi正交多项式的零点作为Hermite插值节点。最后通过多无人机协同欺骗干扰组网雷达的实例测试,表明了所给方法的有效性。更多还原

【Abstract】 At present,in the research of orthogonal collocation method,the control variables and state variables are approximated by Lagrange interpolation polynomials,and the interpolation nodes usually adopt the zeros of Legendre orthogonal polynomials,the derivative information of the state variable can’t be used.Considering that the differential equations of state variables are often involved in optimal control problems,in order to make full use of the derivative information of state variables and reduce the scale of solving the problem,an orthogonal collocation method based on Hermite interpolation is proposed.The state variables are approximated by Hermite interpolation polynomials,and the zeros of Jacobi orthogonal polynomials are used as Hermite interpolation nodes.Finally,the effectiveness of the orthogonal collocation method based on Hermite interpolation is demonstrated by the test of multiple UAV cooperative deception jamming netted radar.更多还原