论文标题
库普曼 - 操作员控制优化，用于空间中的相对运动
A Koopman-Operator Control Optimization for Relative Motion in Space
论文作者
论文摘要
这项工作提出了在Koopman操作员框架中实施的高级最佳控制策略。新技术利用了库普曼表示运动方程解的解，以开发能量最佳逆控制方法。操作员理论可以将有限维度的非线性动力学系统重新将无限尺寸数量的线性系统重新定义。结果，任何非线性动力学的状态表示为高阶正交多项式的线性组合，从而创建了解决方案的状态过渡多项式图。由于可以将最佳控制技术简化为两点边界值问题，因此使用Koopman MAP来及时连接状态和控制变量，以便通过MAP反转和多项式评估获得最佳值。新技术应用于空间中的集合应用，其中两个卫星之间的相对运动以高阶多项式系列扩展为系统的Lagrangian建模，从而使Clohessy-WiltShire方程表示将高阶模型还原为线性截断。
A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal inverse control methodology. The operator theory can reformulate a nonlinear dynamical system of finite dimension into a linear system with an infinite number of dimensions. As a results, the state of any nonlinear dynamics is represented as a linear combination of high-order orthogonal polynomials, which creates the state transition polynomial map of the solution. Since the optimal control technique can be reduced to a two-points boundary value problem, the Koopman map is used to connect the state and control variables in time, such that optimal values are obtained through map inversion and polynomial evaluation. The new technique is applied to rendezvous applications in space, where the relative motion between two satellites is modelled with a high-order polynomial series expansion of the Lagrangian of the system, such that the Clohessy-Wiltshire equations represent the reduction of the high-order model to a linear truncation.
