Structure-preserving optimal control of multibody systems

本研究项目的目标是发展多体系统最优控制的新的数值方法。高能效运动对于节约资源非常重要。具体地说，问题是如何控制特定的多体系统以最大限度地降低能耗。相关的最优控制问题可以通过计算机仿真来解决。例子包括从机器人到生物机械运动系统。另一个例子是航天器的最优姿态控制，该项目的目的是将运动方程数值积分的结构保持格式的概念扩展到最优控制领域。保持结构的数值方法继承了基本力学系统的基本物理性质。由于其固有的物理一致性，结构保持格式通常会导致更好的数值性能。最优控制问题通常也表现出特有的结构特性。然而，到目前为止，这些性质还没有在数值方法的发展中被利用。该研究方案旨在开发满足最优控制问题基本结构性质的新的数值方法。特别是，新提出的最优控制问题的保结构方法应该导致改进的数值稳定性和收敛性质。

The goal of the present research project is to develop new numerical methods for the optimal control of multibody systems. Energy-efficient movements are important to save resources. In particular, the question is how to control a specific multibody system to minimize the energy consumption. The related optimal control problem can be solved by applying computer simulation. Examples range from robotics to biomechanical locomotion systems. Another example is the optimal attitude control of a spacecraft.The aim of the project is to extend the notion of structure-preserving schemes for the numerical integration of the equations of motion to the realm of optimal control. Structure-preserving numerical methods inherit fundamental physical properties from the underlying mechanical system. Due to their inherent pyhsical consistency, structure-preserving schemes typically lead to superior numerical performance.Optimal control problems typically exhibit characteristic structural properties as well. However, so far, these properties have not been exploited in the development of numerical methods. The research proposal aims at the development of new numerical methods which satisfy fundamental structural properties of the optimal control problem. In particular, the newly proposed structure-preserving approach to optimal control problems should lead to improved numerical stability and convergence properties.