三维非完整车辆在球坐标下的逆最优反馈镇定
Inverse Optimal Feedback Stabilization of 3D Nonholonomic Vehicles in Spherical Coordinates
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中文总结 AI 辅助
本文基于球坐标下三维非完整车辆的严格CLFs，提出一种通用逆最优镇定控制器，采用阻尼$L_gV$反馈，通过两种罚函数选择展示灵活性，并验证了性能与约束影响。
中文摘要 AI 辅助
逆最优控制无需求解Hamilton--Jacobi--Bellman (HJB)方程即可提供最优性和鲁棒性保证，但其在三维非完整车辆中的应用一直因缺乏严格控制Lyapunov函数(CLFs)而受阻。近期，在球坐标下为三维非完整车辆构造了此类严格CLFs，在最大可能域上绕过了Brockett障碍。基于这一构造，本文为受浪涌速度、俯仰角速率和偏航角速率驱动的三维非完整车辆开发了一种通用逆最优镇定控制器。该设计是一种阻尼$L_gV$反馈，最小化有意义的代价函数并继承稳定裕度。通过两种罚函数选择展示了其灵活性：状态上的二次运行代价，恢复近经典最优控制公式，以及在用户定义的输入约束下的镇定。数值模拟展示了镇定性能、控制努力权衡以及输入约束的影响。
英文摘要
Inverse optimal control provides optimality and robustness guarantees without solving the Hamilton--Jacobi--Bellman (HJB) equation, but its application to 3D nonholonomic vehicles has been precluded by the absence of strict control Lyapunov functions (CLFs). Recently, such strict CLFs were constructed for the 3D nonholonomic vehicle in spherical coordinates, which circumvent Brockett's obstruction, on the largest possible domain. Building on this construction, this paper develops a general inverse optimal stabilizing controller for the 3D nonholonomic vehicle actuated by surge velocity, pitch rate, and yaw rate. The design is a damping $L_gV$ feedback that minimizes a meaningful cost and inherits stability margins. Its flexibility is demonstrated through two choices of penalty function: a quadratic running cost on the state, recovering a near-classical optimal control formulation, and stabilization under user-defined input constraints. Numerical simulations illustrate stabilization performance, control-effort tradeoffs, and the effect of input constraints.
发表机构
- Department of Mechanical and Aerospace Engineering, UC San Diego（加州大学圣地亚哥分校机械与航空航天工程系）
机构由 AI 辅助整理，请以论文原文为准。
