受控拉格朗日函数方法在力学系统控制中的应用研究

The method of controlled lagrangians (CL) is the way of designing control laws which stabilize mechanical systems. The CL method, by which the stability of systems is analyzed and synthesized from the viewpoint of energy, utilizes and preserves the structural characteristics of the underlying mechanical systems during the designing of the control laws. This makes the method be known for its larger stabilizing convergence region and better robustness. This project, based on the CL method, will study a class of mechanical systems with the lagrangians of kinetic energy minus potential energy, and investigate the control problems beyond the stabilization. This class of mechanical systems covering satellite, various ground vehicles, surface/undersurface crafts, and unmanned aircraft etc, is of wide range of engineering applications background. This study will include the following three aspects. 1. The tracking of the underactuated mechanical systems, investigates how to construct the CL in order to realize the tracking in a manner of stabilizing. For the mechanical systems with symmetry, the various steady motions are achieved in a manner of tracking, i.e., the switching between relative equilibria. 2. The control of the networks of mechanical systems which is formed through communicating connection, solves the problems of stabilizing coordinate motion which keeps the relative positions and/or orientations to be fixed, and generalizes the stabilizing method for a single system to that of multiple systems. 3. The applicability of the CL method will be analyzed when considering the control and communication being constrained; the improved designing method will be investigated.

受控拉格朗日函数（CL）方法是一种镇定力学系统的控制律设计方法。CL法以能量的观点进行稳定性分析与综合，在控制律设计中保留并利用力学系统的结构性质，镇定效果收敛域大，鲁棒性好。本项目针对一类拉格朗日函数为动能减势能的力学系统，基于CL法，开展镇定之外的控制研究。所研究的力学系统包含卫星，各类地面车辆、水面/水下航行器、无人机等，具有广泛的工程应用背景。研究工作包括以下三方面内容：1、欠驱动力学系统的跟踪。研究如何构造时变CL，以镇定的方式实现跟踪；针对具有对称性的力学系统，以跟踪的方式实现各种稳态运动，即相对平衡点之间的切换；2、由通信互联形成的力学系统网络的协调控制，解决力学系统之间相对位置/姿态保持固定的协同运动的镇定问题，将CL法从镇定单个系统推广到协同镇定多个系统；3、在控制输入受限，通信受限的情形下，分析CL法控制方法的适用性，并作相应改进设计。