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由于非线性,最优控制问题通常依赖于数值求解,即通过离散目标泛函和受控运动方程转化为一有限维的非线性最优化问题.最优控制问题中的受控运动方程在表示为受控Birkhoff方程的形式之后,可以利用受控Birkhoff方程的离散变分差分格式进行离散.与按照传统差分格式近似受控运动方程相比,此途径可以诱导更加真实可靠的非线性最优化问题,进而也会诱导更加精确有效的离散最优控制.应用于航天器交会对接问题,该种数值求解最优控制问题的方法在较大时间步长的情况下仍然求得了一个有效实现交会对接的离散最优控制.模拟结果验证了该方法的有效性.
Due to the non-linearity, the optimal control problem usually depends on the numerical solution, that is, it is transformed into a finite-dimensional nonlinear optimization problem by discrete objective functional and controlled equations of motion. The controlled equations of motion in the optimal control problem are expressed in terms of The controlled Birkhoff equation can be discretized using the discretized variational difference scheme of the controlled Birkhoff equation, which leads to a more realistic and reliable nonlinear optimization problem than the approximated controlled equations according to the traditional difference scheme. Which will lead to a more accurate and effective discrete optimal control.Applying to the spacecraft rendezvous and docking problem, this numerical method to solve the optimal control problem still obtains a discrete realization of rendezvous and docking in the case of a large time step Optimal control.The simulation results verify the effectiveness of this method.