...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >A sequential computational approach to optimal control problems for differential-algebraic systems based on efficient implicit Runge-Kutta integration
【24h】

A sequential computational approach to optimal control problems for differential-algebraic systems based on efficient implicit Runge-Kutta integration

机译：基于有效隐式Runge-Kutta积分的微分代数系统最优控制问题的顺序计算方法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Efficient and reliable integrators are indispensable for the design of sequential solvers for optimal control problems involving continuous dynamics, especially for real-time applications. In this paper, optimal control problems for systems represented by index-1 differential-algebraic equations are investigated. On the basis of a time-scaling transformation, the control is parameterized as a piecewise constant function with variable heights and switching time instants. Compared with control parameterization with fixed time grids, the flexibility of adjusting switching time instants increases the chance of finding the optimal solution. Furthermore, error constraints are introduced in the optimization procedure such that the optimal control obtained has a guarantee of integration accuracy. For the derived approximate nonlinear programming problem, a function evaluation and forward sensitivity propagation algorithm is proposed with an embedded implicit Runge–Kutta integrator, which executes one Newton iteration in the limit by employing a predictor-corrector strategy. This algorithm is combined with a nonlinear programming solverIpoptto construct the optimal control solver. Numerical experiments for the solution of the optimal control problem for a Delta robot demonstrate that the computational speed of this solver is increased by a factor of 0.5–2 when compared with the same solver without the predictor-corrector strategy, and increased by a factor of 20–40 when compared with solver embeddingIDAS, the Implicit Differential-Algebraic solver with Sensitivity capabilities developed by Lawrence Livermore National Laboratory. Meanwhile, the accuracy loss compared with the one usingIDASis small and admissible.
机译：对于涉及连续动力学的最优控制问题，尤其对于实时应用而言，高效可靠的积分器对于顺序求解器的设计是必不可少的。本文研究了以指数为1的微分-代数方程表示的系统的最优控制问题。在时间换算的基础上，将控件参数化为具有可变高度和切换时刻的分段常数函数。与具有固定时间网格的控制参数化相比，调整开关时刻的灵活性增加了找到最佳解决方案的机会。此外，在优化过程中引入了误差约束，使得所获得的最优控制具有集成精度的保证。针对导出的近似非线性规划问题，提出了一种功能估计和前向灵敏度传播算法，该算法具有嵌入式隐式Runge-Kutta积分器，该积分器采用预测器-校正器策略在极限内执行一次牛顿迭代。该算法与非线性规划求解器Ipopt结合构成最优控制求解器。 Delta机器人最优控制问题解决方案的数值实验表明，与没有预测器-校正器策略的相同求解器相比，该求解器的计算速度提高了0.5-2倍，并且提高了与求解器embeddingIDAS相比，由劳伦斯·利弗莫尔国家实验室开发的具有敏感功能的隐式微分代数求解器比20–40。同时，与使用IDAS的系统相比，精度损失较小且可以接受。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号