论文标题
通过积分二次约束对合作控制动力学的稳健性能分析
Robust Performance Analysis of Cooperative Control Dynamics via Integral Quadratic Constraints
论文作者
论文摘要
我们使用梯度基于强迫术语来研究合作控制动力学。作为一个具体示例，我们专注于嵌入在未知标量字段中的车辆的源寻求动力学，其中包含一部分具有梯度信息的代理。作为相互作用机制，考虑了形成控制动力学和羊群动力学。我们利用$α$ - 综合二次约束的框架，只要可以实现指数稳定性，就可以获得收敛率估计。假定通信图和相互作用势是时间不变和不确定的。足够的条件采用与网络大小无关的线性矩阵不平等的形式。给出了所谓的\ textit {hard} Zames-falb $α$ -IQC的推导（纯粹是在时间域中），涉及一般非cusal高级乘数的Zames-falb $α$ -IQC，以及将乘数与$α$ -IQC设置的乘数合适的参数化。时间域参数有助于直接扩展到线性参数变化的系统。数值示例说明了理论结果的应用。
We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As interaction mechanisms, formation control dynamics and flocking dynamics are considered. We leverage the framework of $α$-integral quadratic constraints to obtain convergence rate estimates whenever exponential stability can be achieved. The communication graph and the interaction potential are assumed to be time-invariant and uncertain. Sufficient conditions take the form of linear matrix inequalities independent of the size of network. A derivation (purely in time-domain) of the so-called \textit{hard} Zames-Falb $α$-IQCs involving general non-causal higher order multipliers is given along with a suitably adapted parameterization of the multipliers to the $α$-IQC setting. The time-domain arguments facilitate a straightforward extension to linear parameter varying systems. Numerical examples illustrate the application of the theoretical results.
