基于能量整形的随机Lagrange系统的切换控制

This project studies the modeling and switching control problems for stochastic Lagrange systems based on energy modification. Lagrange system has always attracted extensive attention in the control field due to its realizable construction and wide applications. However, the random disturbance and the switching behavior lead to the difficulty of the research. The time derivative for each active subsystem acting on Lyapunov function is relaxed to be indefinite with the help of uniformly stable function. Improved criteria on uniformly asymptotic stability for switched stochastic nonlinear systems are proposed by applying the weakened condition. The theorems obtained in the project will develop and refine the existing switched stochastic systems theories, and will be the foundation of nice controller design. From two aspects: mathematical idealization and physical correctness, the modelings of Lagrange systems driven by white noise and by color noise are presented respectively. Choosing energy modified functions as Lyapunov functions, based on the obtained theorems, the state-driven switching and time-driven switching controllers are respectively designed by using vectorial backstepping method. The combination of strict stochastic analysis and applicability of the switching controller will provide feasible scheme to solve control problems of practical systems.

本项目基于能量整形研究随机噪声干扰下Lagrange系统的建模与切换控制问题。Lagrange系统因其理想结构和实用上的普适性，一直受到控制界的广泛关注。随机干扰和切换行为增加了Lagrange系统建模和控制的难度。我们首先借助一致稳定函数将随机Lyapunov函数沿每个子系统的导数放宽为不定的，给出较宽松的判定切换随机系统一致渐近稳定性的条件。这将进一步丰富和完善切换随机系统理论，并为设计具有良好性能的控制器奠定基础。其次从数学理想化和物理正确性两个方面考虑，分别对白噪声和有色噪声干扰下的Lagrange系统进行建模。以能量整形函数为Lyapunov函数，基于所建立的一致渐近稳定性理论，利用向量反推技术分别给出状态驱动切换和时间驱动切换控制器的设计。本项目同时综合了随机分析的严密性和切换控制的实用性特点，为解决实际系统的控制问题提供可行的方案。

本项目围绕切换随机非线性系统的一致渐近稳定性分析，随机振动环境下Lagrange系统的建模与切换控制策略的设计问题进行了深入的研究。利用一致稳定函数和模型依赖平均驻留时间技术发展了切换随机非线性系统的一致渐近稳定性的理论判据。基于实用性和普适性，合理利用有色噪声建立随机振动环境下的机械系统和机器人系统的随机Euler-Lagrange运动方程。综合利用能量整形函数、向量式反推方法、自适应滑模控制、切换控制等方法，根据不同的目标设计相应的控制器达到期望的目标。将相关研究结果应用到振动环境下的6-自由度斯坦福机械手抓取物体的轨迹规划和轨迹跟踪控制问题中。通过逆运动学分析将末端执行器在任务空间中的位移转化为关节空间中的关节位移，从而规划出一种特殊的光滑连续轨迹。利用对任务空间的合理划分，设计了一种新颖的基于自适应滑模的多级状态驱动切换控制策略。本项目所获得的成果将对振动环境下的机电一体化系统的控制提供理论指导。

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