可达性、生存性和不变性问题的统一求解框架
A Novel Unified Framework for Solving Reachability, Viability and Invariance Problems
摘要：
水平集方法是求解可达性和不变性问题的一种常用工具。然而，由于耗散函数的处理和Hamilton-Jacobi偏微分方程终端条件的构造困难，限制了水平集方法在非仿射非线性系统和不规则目标集问题中的应用。本文提出的方法可以有效地避免上述棘手的问题，从而具有更好的通用性。该方法利用值函数的非零子水平集来刻画具有不同时间范围的可达集或不变集。该值函数不是通过求解偏微分方程的粘性解而获得的，而是通过递归和插值逼近而获得的。最后通过实例说明了该方法的准确性和通用性。
英文摘要：
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the Hamilton-Jacobi partial differential equation, limit the application of the level set method in some problems with non-affine nonlinear systems and irregular target sets. This paper proposes a method that can effectively avoid the above tricky issues and thus has better generality. In the proposed method, the reachable or invariant sets with different time horizons are characterized by some non-zero sublevel sets of a value function. This value function is not obtained by solving a viscosity solution of the partial differential equation but by recursion and interpolation approximation. At the end of this paper, some examples are taken to illustrate the accuracy and generality of the proposed method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
