Title: Contraction Theory with Inequality Constraints Show Chinese title

Title: 带有不等式约束的收缩理论

Abstract: This paper extends continuous contraction theory of nonlinear dynamical systems to systems with nonlinear inequality constraints. It shows that the contraction behaviour of the constrained dynamics is given by the covariant derivative of the system dynamics from the original contraction theorem [4], plus the second covariant derivative of the active inequality constraint. Practical applications include controllers constrained to an operational envelope, trajectory control with moving obstacles, and a classical Lagrangian interpretation of the single and two slit experiments of quantum mechanics. Show Chinese abstract

Abstract: 本文将非线性动力系统的连续收缩理论扩展到具有非线性不等式约束的系统。 它表明，受约束的动力学的收缩行为由原始收缩定理[4]中系统动力学的协变导数加上活动不等式约束的二阶协变导数给出。 实际应用包括受限于操作包络的控制器、带有移动障碍物的轨迹控制，以及量子力学中单缝和双缝实验的经典拉格朗日解释。