Feedback control design and model reduction for strongly nonlinear systems

强非线性系统的反馈控制设计和模型简化

• 批准号: 138352-2013
• 负责人: Michalska, Hannah
• 金额: $ 2.11万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=659735
• 关键词: Feedback; control; design; model; reduction

In an attempt to bridge the gap between nonlinear control theory and practice, in the next five years, the proposed research program will seek to address the problem of reduction of nonlinear system complexity for the purpose of control design implementation. Since multi-body dynamical systems pose many challenging nonlinear control problems, the reference systems under study is the class of controlled Hamiltonian or Lagrangian mechanical systems with constraints. Examples include stabilizing control of vertical structures such as standing or walking humans. With this goal in mind the research program is summarized as follows: **(A) Development of a systematic framework for control-oriented modeling, nonlinear control problem simplification and reduction for strongly nonlinear systems, with reference to the class of system considered. Strongly nonlinear systems are these which do not lend themselves to control design and analysis via linearization approaches. The principal objectives in control problem simplifcation are to facilitate: (i) assessment of stabilizability and reachability regions for a given class of admissible control inputs, (ii) construction of semi-global stablilizing feedback laws with the emphasis on real-time application regimes. **(B) Development of computationally tractable, semi-global nonlinear control design approaches that can be applied to stabilization of vertical structures in potential felds and locomotion control of multi-body systems under actuation and mobility constraints. The envisaged design approaches will employ the concepts of invariance under transformations and energy conversion and balancing rather than energy shaping. The proposed methods for combined modeling and control will employ the spatial operator algebra as a modern and powerful tool for computational complexity reduction in mechanical system design, control, and analysis.** Applications include advanced robotic control design, spatial models for postural balance aiming at quantitative prediction of loss of balance in humans, and other problems in biomechanics.**************************

为了弥合非线性控制理论与实践之间的差距，在未来五年内，拟议的研究计划将寻求解决降低非线性系统复杂性的问题，以实现控制设计的目的。由于多体动力学系统提出了许多具有挑战性的非线性控制问题，因此所研究的参考系统是一类带约束的受控哈密顿或拉格朗日力学系统。例如稳定对垂直结构的控制，如站立或行走的人。考虑到这一目标，研究方案总结如下：**(A)参照所考虑的系统类别，为强非线性系统的面向控制的建模、非线性控制问题的简化和降阶开发一个系统框架。强非线性系统是指那些不适合通过线性化方法进行控制设计和分析的系统。控制问题简化的主要目的是：(I)对于给定的一类允许的控制输入，评估其可镇定和可达区域；(Ii)构造半全局镇定反馈律，重点是实时应用机制。**(B)发展易于计算的半全局非线性控制设计方法，可应用于位场中垂直结构的稳定和多体系统在驱动和运动约束下的运动控制。设想的设计方法将采用变换下的不变性和能量转换和平衡的概念，而不是能量成形的概念。提出的组合建模和控制方法将使用空间算子代数作为一种现代和强大的工具，用于降低机械系统设计、控制和分析中的计算复杂性。**应用包括先进的机器人控制设计、旨在定量预测人体失去平衡的姿势平衡的空间模型，以及生物力学中的其他问题。