论文标题
使用控制屏障功能的强大不变性：Clarke切线锥方法
Strong Invariance Using Control Barrier Functions: A Clarke Tangent Cone Approach
论文作者
论文摘要
许多控制应用程序要求将系统限制在特定状态集，通常称为安全集。渲染安全集的一种实用而灵活的方法，涉及使用控制屏障功能和二次编程方法计算控制输入。然而，许多先前的结果都要求由此产生的控制输入是连续的，这需要强大的假设，或者很难在理论上证明。在本文中，我们使用差分包含方法来证明可以使用不连续的控件输入来实现多个集合不变性。我们提出了一个优化公式，该公式计算此类控制输入，并且可以以多种形式提出，包括可行性问题，线性程序或二次程序。此外，我们讨论了优化问题是可行的条件，并表明可测量的优化问题的任何可行解决方案均可使多个安全集向前不变。
Many control applications require that a system be constrained to a particular set of states, often termed as safe set. A practical and flexible method for rendering safe sets forward-invariant involves computing control input using Control Barrier Functions and Quadratic Programming methods. Many prior results however require the resulting control input to be continuous, which requires strong assumptions or can be difficult to demonstrate theoretically. In this paper we use differential inclusion methods to show that simultaneously rendering multiple sets invariant can be accomplished using a discontinuous control input. We present an optimization formulation which computes such control inputs and which can be posed in multiple forms, including a feasibility problem, a linear program, or a quadratic program. In addition, we discuss conditions under which the optimization problem is feasible and show that any feasible solution of the considered optimization problem which is measurable renders the multiple safe sets forward invariant.
