输出反馈条件下的欧拉-拉格朗日系统协同控制的全局稳定性研究

欧拉-拉格朗日系统具有本质非线性以及状态强耦合，这就给仅能利用（位置）输出反馈的全局稳定的协同控制器设计带来极大的挑战。为此，本项目首先通过坐标转换和求解微分方程组，重构出不可测状态的部分线性化解耦模型，设计速度观测器，最终证明基于输出反馈的跟踪控制的一致全局渐进稳定性。进而，受建筑学中tensegrity结构启发，优化设计出具有稀疏、全局稳定性质的全局刚性tensegrity结构，并在虚拟tensegrity结构框架下，设计出欧拉-拉格朗日系统的分布式编队控制器，解决了任意构型编队控制的全局稳定问题。最后，针对欠驱动欧拉-拉格朗日系统的编队控制问题，基于无源性理论得到非直接驱动状态的解析模型，设计出高增益速度观测器和分布式编队控制器，并利用奇异摄动理论证明其全局稳定性。本项目解决了输出反馈条件下的欧拉-拉格朗日系统协同控制的全局稳定性问题，其成果可推广至其他全/欠驱动系统的协同控制。

It is of great challenge to design distributed output feedback controllers for multiple Euler-Lagrange systems such that the system is globally stable due to the intrinsic nonlinearities and state couplings. In order to overcome these difficulties, we propose a new control framework that starts with reconstructing a partial linear decoupling model with respect to unmeasurable states through coordinate transformation and solving partial differential equations. Based on the model, we develop a new class of velocity observers, then the uniformly globally asymptotical stability for output feedback tracking control can be realized. Furthermore, inspired by the stable tensegrity structure in architecture, we develop an algorithm on how to construct sparse and global rigid tensegrity for arbitrary given configurations. By employing the virtual tensegrity structure, we come up with globally stable formation controllers for multiple Euler-Lagrange systems to achieve arbitrary geometric shapes. Finally, to solve the distributed formation control problem for under-actuated Euler-Lagrange systems, we apply the passivity theory to obtain the analytical model for under-actuated states, based on which the high gain velocity observer and distributed controllers are respectively proposed, resulting in the global stability verified by singular perturbation theory. The results derived in our project on coordinating the multi Euler-Lagrange systems to achieve global stability can be extended to the output feedback coordinated control problems for any other fully/under-actuated systems.