论文标题
参考依赖性不变集：基于正方形的计算和在受约束控制中的应用总和
Reference Dependent Invariant Sets: Sum of Squares Based Computation and Applications in Constrained Control
论文作者
论文摘要
本文的目的是提出一种系统的方法，以计算受约束约束的系统的依赖性依赖的积极不变集。为此，我们首先将这些集合描述为参考依赖性Lyapunov函数的级别集。基于此特征和使用正方形总和（SOS）理论，我们为存在集合的存在提供了多项式证书。随后，通过一些代数操作，我们根据半明确编程（SDP）问题表达此证书，该问题最大化了所得参考依赖性不变集的大小。然后，我们向示例系统实施了提出的方法的结果，并提出了所提出的方法的一些变化，这些方法可能有助于减少该方法的数值问题。最后，在模型预测控制（MPC）中采用了所提出的方法来计算终端集，并在显式参考调查员（ERG）方案中用于计算所谓的动态安全余量（DSM）。通过模拟研究证明了所提出的方法在每个方案中的有效性。
The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares (SOS) theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming (SDP) problem which maximizes the size of the resulting reference dependent invariant sets. We then present the results of implementing the proposed method to an example system and propose some variations of the proposed method that may help in reducing the numerical issues of the method. Finally, the proposed method is employed in the Model Predictive Control (MPC) for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor (ERG) scheme to compute the so-called Dynamic Safety Margin (DSM). The effectiveness of the proposed method in each of the schemes is demonstrated through a simulation study.
