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，在接下来的五年中，拟议的研究计划将寻求解决非线性系统复杂性的降低问题，以进行控制设计实施。由于多体动力学系统构成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受限制的受控汉密尔顿或拉格朗日机械系统的类别。例子包括稳定对垂直结构（例如站立或行走人类）的控制。考虑到这个目标，研究计划的总结如下：**（a）开发用于控制的导向建模，非线性控制问题简化和强烈非线性系统的减少的系统框架，参考了所考虑的系统类别。强烈的非线性系统是通过线性化方法来控制设计和分析的这些系统。控制问题简化的主要目标是促进：（i）评估给定的一类可允许的控制输入的稳定性和可及性区域，（ii）构建半全球稳定反馈法，重点是实时应用程序。 **（b）开发计算上可进行的半全球非线性控制设计方法，可应用于在驱动和移动性约束下对潜在长石和多体系统的运动控制中垂直结构的稳定。所设想的设计方法将采用变换，能量转换和平衡而不是能量塑造的概念。提出的组合建模和控制的方法将利用空间操作员代数作为机械系统设计，控制和分析的计算复杂性降低计算复杂性的现代化和强大工具。