Feedback control design and model reduction for strongly nonlinear systems

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。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，所研究的参考系统是一类受控哈密顿或拉格朗日力学系统的约束。例子包括垂直结构的稳定控制，如站立或行走的人。考虑到这一目标，研究计划概述如下：**（A）开发一个系统框架，用于面向控制的建模，非线性控制问题的简化和减少强非线性系统，参考所考虑的系统类别。强非线性系统是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标是便于：（i）对给定的一类容许控制输入的可镇定性和可达性区域的评估，（ii）半全局稳定反馈律的构造，重点是实时应用制度。**（B）开发计算上易于处理的半全局非线性控制设计方法，可应用于潜在领域中的垂直结构的稳定以及致动和移动性约束下的多体系统的运动控制。设想的设计方法将采用变换下的不变性概念以及能量转换和平衡，而不是能量成形。所提出的建模和控制相结合的方法将采用空间算子代数作为一种现代而强大的工具，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，旨在定量预测人类失去平衡的姿势平衡空间模型，以及生物力学中的其他问题。

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.**************************