标题： 数据驱动的不确定非线性系统的运动规划 显示英文标题

标题： Data-Driven Motion Planning for Uncertain Nonlinear Systems

摘要： 本文提出了一种数据驱动的运动规划框架，用于非线性系统，该框架构建了一系列重叠的不变多面体序列。 在每个随机采样的航点周围，算法识别一个凸允许区域，并求解数据驱动的线性矩阵不等式问题，以学习多个椭球不变集及其局部状态反馈增益。 这些椭球的凸包，在通过插值增益获得的分段仿射控制器下仍保持不变，然后通过一个多面体进行近似。 通过验证连续凸包多面体的交集并引入中间节点以实现平滑过渡，确保节点之间的安全过渡。 控制增益通过基于单形的插值实时进行，从而在整个运动过程中保持状态在不变多面体内。 与依赖系统动态模型的传统方法不同，我们的方法仅需数据即可计算安全区域并设计状态反馈控制器。 该方法通过仿真得到验证，展示了所提出方法在为复杂非线性系统实现安全且动态可行路径方面的有效性。 显示英文摘要

摘要： This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and solves data-driven linear-matrix-inequality problems to learn several ellipsoidal invariant sets together with their local state-feedback gains. The convex hull of these ellipsoids, still invariant under a piece-wise-affine controller obtained by interpolating the gains, is then approximated by a polytope. Safe transitions between nodes are ensured by verifying the intersection of consecutive convex-hull polytopes and introducing an intermediate node for a smooth transition. Control gains are interpolated in real time via simplex-based interpolation, keeping the state inside the invariant polytopes throughout the motion. Unlike traditional approaches that rely on system dynamics models, our method requires only data to compute safe regions and design state-feedback controllers. The approach is validated through simulations, demonstrating the effectiveness of the proposed method in achieving safe, dynamically feasible paths for complex nonlinear systems.