论文标题
基于凸面线性拟合的线性系统的数据驱动的控制不变设置的近似
Data-driven approximation of control invariant set for linear system based on convex piecewise linear fitting
论文作者
论文摘要
控制不变集对于保证安全控制至关重要，并且通过使用数据驱动的方法来重新审视用于线性离散时间系统的计算控制不变设置的问题。具体而言，记录了线性MPC收敛轨迹上的样品点，其中凸船体为线性系统制定了控制不变设置。为了近似多个样品点的凸壳，已经提出了凸面分段线性（PWL）拟合框架，该框架产生具有预定义复杂性的多面体近似值。还开发了用于凸PWL拟合问题的下降算法，该算法可以保证会收敛到局部最佳。提出的策略在计算以预定义的复杂性高维设置的控制不变设置方面具有灵活性。仿真结果表明，提出的数据驱动近似可以以高精度和相对较低的计算成本计算近似控制不变设置。
Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on convergent trajectories of linear MPC are recorded, of which the convex hull formulates a control invariant set for the linear system. To approximate the convex hull of multiple sample points, a convex piecewise linear (PWL) fitting framework has been proposed, which yields a polyhedral approximation with predefined complexity. A descent algorithm for the convex PWL fitting problem is also developed, which is guaranteed to converge to a local optimum. The proposed strategy is flexible in computing the control invariant set in high dimension with a predefined complexity. Simulation results show that the proposed data-driven approximation can compute the approximated control invariant set with high accuracy and relatively low computational cost.
