论文标题
用于完全分布的非线性最佳控制的稀疏多性LPV控制器
A Sparse Polytopic LPV Controller for Fully-Distributed Nonlinear Optimal Control
论文作者
论文摘要
在本文中，我们处理了图形上非线性动力学系统的分布式最佳控制，即大规模系统，每个子系统的动力学仅取决于相邻状态。从以前的工作从我们设计基于云的部分分布的解决方案开始，在这里我们提出了一种完全分布的算法。本文中该方法的主要新颖性是设计稀疏控制器，以稳定分布式算法的每种迭代中的非线性系统的轨迹。所提出的控制器基于稳定控制器的设计，用于多型线性参数变化（LPV）系统，可满足非convex稀疏约束。得益于适当的顶点矩阵以及使用非凸立矩阵问题的凸近似的迭代过程，我们能够设计一个控制器，在该控制器中，每个代理可以通过简单地结合一些可以预先计算出离线的顶点矩阵的系数来局部计算每种迭代的反馈收益。我们显示了该策略对在多代理形成控制问题上进行的模拟的有效性。
In this paper we deal with distributed optimal control for nonlinear dynamical systems over graph, that is large-scale systems in which the dynamics of each subsystem depends on neighboring states only. Starting from a previous work in which we designed a partially distributed solution based on a cloud, here we propose a fully-distributed algorithm. The key novelty of the approach in this paper is the design of a sparse controller to stabilize trajectories of the nonlinear system at each iteration of the distributed algorithm. The proposed controller is based on the design of a stabilizing controller for polytopic Linear Parameter Varying (LPV) systems satisfying nonconvex sparsity constraints. Thanks to a suitable choice of vertex matrices and to an iterative procedure using convex approximations of the nonconvex matrix problem, we are able to design a controller in which each agent can locally compute the feedback gains at each iteration by simply combining coefficients of some vertex matrices that can be pre-computed offline. We show the effectiveness of the strategy on simulations performed on a multi-agent formation control problem.
