论文标题
具有概率安全限制的导航：凸配方
Navigation with Probabilistic Safety Constraints: Convex Formulation
论文作者
论文摘要
我们考虑具有安全限制的导航问题。安全限制是概率的，其中给定的集合被分配了一定程度的安全性，一个零和一个之间的数字，零是安全的，一个是不安全的。确定性的不安全集将作为对安全性概率描述的特殊情况。我们通过概率安全限制为导航问题提供凸公式。通过使用涉及Perron-Frobenius和Koopman操作员的线性转移操作者理论方法在密度的双重空间中提出导航问题，从而使凸公式成为可能。凸制配方导致概率安全验证和控制设计的无限维度可行性问题。优化问题的有限维近似取决于线性传输操作员的数据驱动近似。
We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The deterministic unsafe set will arise as a particular case of the proposed probabilistic description of safety. We provide a convex formulation to the navigation problem with probabilistic safety constraints. The convex formulation is made possible by lifting the navigation problem in the dual space of density using linear transfer operator theory methods involving Perron-Frobenius and Koopman operators. The convex formulation leads to an infinite-dimensional feasibility problem for probabilistic safety verification and control design. The finite-dimensional approximation of the optimization problem relies on the data-driven approximation of the linear transfer operator.
