论文标题
基于安全性学习的基于不确定性依赖性约束的系统的控制（扩展版）
Safety-Aware Learning-Based Control of Systems with Uncertainty Dependent Constraints (extended version)
论文作者
论文摘要
安全地学习和控制动态系统的问题 - 即稳定最初（部分）未知系统的同时确保其不留下规定的“安全集”的问题 - 最近在控件社区中受到了极大的关注。但是，当保险箱的结构本身取决于系统动力学的未知部分时，就会出现进一步的复杂性。特别是，一种基于控制Lyapunov功能（CLF），控制障碍功能（CBF）和高斯流程（以建立未知术语设置的置信度）的流行方法，事实证明，该方法在已知的安全设置设置中成功地取得了成功，由于效率低下的AS-IS，由于仅使用系统状态测量值估算和限制了较高的可能性。在本文中，我们基于有关GP和复制内核的最新文献来执行后一个任务，并展示如何相应地修改基于CLF-CBF的方法以获得安全保证。也就是说，我们得出了指数的CLF和第二相对顺序指数CBF约束，其满足保证了具有很高概率的部分未知安全集的稳定性和向前的变异。为了克服这些条件在连续域上的验证的无礼性，我们应用了状态空间的离散化，并使用Lipschitz的连续性属性在离散状态空间中得出等效的CLF和CBF证书。最后，我们使用派生证书提出了一种用于控制设计目标的算法。
The problem of safely learning and controlling a dynamical system - i.e., of stabilizing an originally (partially) unknown system while ensuring that it does not leave a prescribed 'safe set' - has recently received tremendous attention in the controls community. Further complexities arise, however, when the structure of the safe set itself depends on the unknown part of the system's dynamics. In particular, a popular approach based on control Lyapunov functions (CLF), control barrier functions (CBF) and Gaussian processes (to build confidence set around the unknown term), which has proved successful in the known-safe set setting, becomes inefficient as-is, due to the introduction of higher-order terms to be estimated and bounded with high probability using only system state measurements. In this paper, we build on the recent literature on GPs and reproducing kernels to perform this latter task, and show how to correspondingly modify the CLF-CBF-based approach to obtain safety guarantees. Namely, we derive exponential CLF and second relative order exponential CBF constraints whose satisfaction guarantees stability and forward in-variance of the partially unknown safe set with high probability. To overcome the intractability of verification of these conditions on the continuous domain, we apply discretization of the state space and use Lipschitz continuity properties of dynamics to derive equivalent CLF and CBF certificates in discrete state space. Finally, we present an algorithm for the control design aim using the derived certificates.
