凸优化理论在非线性滚动时域控制中的应用

Convex Optimization Theory Applied to Nonlinear Receding Horizon Control

滚动时域控制是一种考虑整个固定时域范围的控制方法,对于每次由优化算法得到的最优控制序列,仅取序列中的第一个元素作为当前此时刻的控制率。滚动时域控制是一种基于模型、滚动优化并结合反馈校正的优化控制算法。在由控制自由变量的非线性函数组成的非线性优化问题中,该控制自由变量的求取可采用凸优化理论中的相关算法来获取,进而采用滚动时域的思想来重新组合控制变量,以得到最优的控制变量。对于非线性系统中滚动时域控制所得到的最优化问题,分析非线性系统的滚动时域控制是否存在最优解,利用凸优化理论中的基本知识分别推导出此最优化问题在无和有集合约束条件下存在最优解的充要条件,并将此充要条件与经典优化理论中现有的最优条件进行对比,得出该充要条件的优势,最后将凸优化理论在无人机航迹规划算例中进行仿真验证。

Receding Horizon Control （RHC） is a control method which is applied in a whole fixed horizon range. The RHC chooses the first element as the current control law among the optimum control sequences obtained by any optimization algorithms. The RHC is an optimization control algorithm based on the model, receding optimization and feedback tuning. For a nonlinear optimization problem composed of a nonlinear function coming from some control free variables, the free variables can be derived by many correspond algorithms in convex optimization theory. After we used the ideas of the receding horizon to reassemble the obtained control variables, the optimum control variable sequence was gained. To the nonlinear optimum problem in receding horizon control design, we analyzed whether there was an optimum solution in nonlinear system＇s receding horizon control. Based on the principle theory in convex optimization, we derived two necessary and sufficient conditions of the optimum solution between set constrains and no set constrains. Then we compared these two necessary and sufficient conditions with classical FJ condition so as to advantage efficiency of this condition. Finally we applied the theoretical results in path planning of UAV of the analysis was verified. get the and the