Theory and Methods of Control and Optimization of Dynamical Systems for Engineering Applications

工程应用动力系统控制与优化理论与方法

• 批准号: 448676431
• 负责人: Professor Dr. Hans Georg Bock
• 金额: --
• 依托单位: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/448676431?language=en
• 关键词: Theory; Methods; Control; Optimization; Dynamical

This German-Russian collaboration project aims at the development of both analytical and numerical methods for optimization and optimal control of certain classes of dynamical processes, proposed and studied by the Russian partners, which exhibit complex characteristic properties important for engineering applications. Robotic locomotion in resistive environment without external forces only by moving internal masses or configuration changes leads to mechanical control problems with state-dependent discontinuities, especially due to Coulomb friction, and numerous control and state constraints. Underactuated multibody systems with visco-elastic components, only partially measurable states, uncertain system parameters and external perturbations call for fast feedback control laws to achieve high-precision positioning. Fuel efficient flight planning of high-speed (supersonic) passenger aircraft leads to complex models of longhorizon mixed-integer control problems with numerous state and control constraints accounting for technical restrictions and passenger comfort and safety. In order to meet these particular requirements new analytical and numerical optimal control methods will be developed. The Heidelberg team will consider the relatively general class of nonlinear optimal control problems (OCP) with integer-valued controls and governed by ODE or DAE subject to boundary conditions and state and control constraints. The right hand sides of the dynamics may be discontinuous at zeros of state-dependent switching functions, arising particularly from Coulomb friction. In principle, such optimal control problems can be solved by extensions of Pontryagin’s Maximum Principle (PMP). However, in the above case the indirect PMP results in multipoint boundary value problems with switching functions and additional jumps in the adjoint variables, which are extremely difficult to solve. The proposed project will therefore build on the direct multiple shooting approach developed by the Heidelberg group to solve such problems numerically. Two ways to handle Coulomb friction will be developed, a “forward integration” approach and a novel “disjunctive programming” method. For systems with uncertainties, optimal feedback controls will be computed by fast multilevel iterations for “Nonlinear Model Predictive Control” combined with “Moving Horizon Estimation”, which will be generalized to the general OCP class above. We will develop a new analytical approach to derive fast, locally valid, piecewise affine feedback control laws, which will significantly reduce sampling times further, compare it to the PMP approach to compute “neighbouring feedback” controls, and develop possible cross-over techniques. The development of the dedicated new numerical methods will go hand in hand with analysis and solution of the challenging engineering problems and will be conducted in close cooperation of the Moscow and the Heidelberg team.

这个德国-俄罗斯合作项目旨在开发分析和数值方法，用于俄罗斯合作伙伴提出和研究的某些类别的动态过程的优化和最佳控制，这些过程具有对工程应用重要的复杂特性。机器人在无外力环境中的运动仅通过移动内部质量或配置变化导致具有状态依赖不连续性的机械控制问题，特别是由于库仑摩擦以及许多控制和状态约束。欠驱动多体系统具有粘弹性元件、部分可测状态、系统参数不确定性和外部扰动，需要快速反馈控制律来实现高精度定位。高速（超音速）客机的燃油效率飞行规划导致了复杂的模型longhorizon混合整数控制问题，许多国家和控制的限制占技术限制和乘客的舒适性和安全性。为了满足这些特殊的要求，将开发新的分析和数值最优控制方法。海德堡团队将考虑相对一般的一类非线性最优控制问题（OCP），这些问题具有整数值控制，并受边界条件以及状态和控制约束的ODE或DAE控制。动态的右手边可能是不连续的状态依赖的开关函数，特别是库仑摩擦引起的零点。原则上，这样的最优控制问题可以通过扩展庞特里亚金最大值原理（PMP）来解决。然而，在上述情况下，间接PMP的结果在多点边值问题的切换功能和额外的跳跃的伴随变量，这是非常难以解决的。因此，拟议的项目将建立在海德堡小组开发的直接多次射击方法的基础上，以数值方式解决这些问题。两种方法来处理库仑摩擦将开发，一个“前向积分”的方法和一个新的“析取编程”的方法。对于具有不确定性的系统，最优反馈控制将通过“非线性模型预测控制”与“滚动时域估计”相结合的快速多层迭代来计算，这将推广到上述一般的OCP类。我们将开发一种新的分析方法，以获得快速，局部有效，分段仿射反馈控制律，这将显着减少采样时间进一步，比较它的PMP方法来计算“相邻的反馈”控制，并开发可能的交叉技术。专用的新数值方法的开发将与具有挑战性的工程问题的分析和解决齐头并进，并将在莫斯科和海德堡团队的密切合作下进行。