论文标题
基于控制屏障功能的梯度流设计，用于受约束的非线性编程
Control Barrier Function Based Design of Gradient Flows for Constrained Nonlinear Programming
论文作者
论文摘要
本文考虑了设计连续时间动力系统的问题，该系统解决了约束的非线性优化问题，并使可行的前进不变和渐近稳定。可行集合的不变性随时将动态视为算法时，这意味着它返回可行的解决方案，无论何时终止。我们的方法通过由约束功能定义的输入来增强目标函数的梯度流，将可行的集合视为安全集，并使用控制屏障函数理论中的技术合成安全反馈控制器。所得的闭环系统（称为安全梯度流）可以看作是原始偶偶，该状态对应于原始变量，并且输入对应于双重变量。我们根据约束资格提供详细的条件套件，根据该条件（隔离和非分离）局部最小化器相对于可行集合和整个状态空间都是稳定的。在一个简单的示例中，与其他连续时间方法进行优化的比较说明了安全梯度流的优势。
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning it returns a feasible solution regardless of when it is terminated. Our approach augments the gradient flow of the objective function with inputs defined by the constraint functions, treats the feasible set as a safe set, and synthesizes a safe feedback controller using techniques from the theory of control barrier functions. The resulting closed-loop system, termed safe gradient flow, can be viewed as a primal-dual flow, where the state corresponds to the primal variables and the inputs correspond to the dual ones. We provide a detailed suite of conditions based on constraint qualification under which (both isolated and nonisolated) local minimizers are stable with respect to the feasible set and the whole state space. Comparisons with other continuous-time methods for optimization in a simple example illustrate the advantages of the safe gradient flow.
