Introduction to nonlinear optimal control
Introduction to nonlinear optimal control
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非线性最优控制简介
DOI：
10.1007/11583592_1
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
B. Bonnard;Jean
极大值原理以弱形式和一般形式呈现。标准样张详细，并与数值分辨率的拍摄方法进行了联系。还简要介绍了极值的微观局部分析。关于二阶条件，小的时间最优性通过高阶广义变化来解决。对于极值的局部最优性，针对常规问题和最小时间奇异单输入仿射控制系统，引入了共轭点理论。将分析应用于开普勒方程的最小时间控制，并给出了相应的轨道转移问题的数值模拟。对于状态约束最优控制问题，给出了边界弧的必要条件。结和反射条件是在黎曼情况下导出的。
The maximum principle is presented in the weak and general forms. The standard proofs are detailed, and the connection with the shooting method for numerical resolution is made. A brief introduction to the micro-local analysis of extremals is also provided. Regarding second-order conditions, small time-optimality is addressed by means of high order generalized variations. As for local optimality of extremals, the conjugate point theory is introduced both for regular problems and for minimum time singular single input affine control systems. The analysis is applied to the minimum time control of the Kepler equation, and the numerical simulations for the corresponding orbit transfer problems are given. In the case of state constrained optimal control problems, necessary conditions are stated for boundary arcs. The junction and reflection conditions are derived in the Riemannian case.