含终端等式约束LQ时变控制器设计的新方法

对于LQ终端约束控制问题，利用所引入的Lagrange乘子是常数的本质，构造了新的两区段形式的终端控制器，避免了传统控制器在靠近终端区段时反馈增益矩阵过大、甚至奇异的缺点，而且两个区段的控制律都具有反馈一前馈结构；对求解终端控制器问题的变分原理做了改进，分析了新变分式中的软约束项与反馈增益矩阵之间的联系，指出它对于构造反馈结构的控制器，尤其是对最小能量控制问题，具有重要的意义．进一步，利用区段混合能理论中的能量矩阵，构造了终端控制器的矩阵Riccati微分方程组的闭合解．最后，通过求解一个航天器交会最优控制问题，检验了本文所设计的LQ终端约束控制器的有效性及优越性．

A new approach to LQ time-varying controllers with terminal equality constraints

A two-interval LQ terminal controller is constructed by using the fact that the Lagrange multiplier of the variational principle is a constant. The new terminal controller not only overcomes the drawbacks that the feedback gains of conventional LQ terminal controllers tend to infinity when close to the final time, but also keeps a feedback- feedforward structure. The variational principle for the LQ terminal control problem is also improved by adding a soft constraint. Relation between the ＂soft term＂ and the feedback gain is presented that the ＂soft term＂ is an enhancer to improve the performance of the controller, especially for minimum energy control problems. Further more, based on the interval mixed energy theory, closed form solutions of generalized Riccati transformation matrices are given. Advantages of the proposed two-interval terminal controller and effectiveness of the closed-form solutions are verified by numerical examples of an optimal rendezvous problem of spacecrafts.