带偏挂拖车的非完整汽车模型的镇定
Stabilization of a Nonholonomic Car Model with Off-Hooked Trailers
AI总结：
本文研究带两个偏挂拖车的非完整汽车模型，通过幂零近似和含振荡分量的时变反馈控制器，克服 Brockett 条件限制，实现系统指数镇定。
摘要：
我们考虑一个受控汽车带两个拖车的运动学模型，假设每个拖车连接在前一车轴后方一定距离处（“偏挂拖车”）。针对该模型，我们推导出向特权坐标的变换，并给出相应的幂零拟齐次近似系统。该幂零近似的各分量以原系统的力学参数显式表示。所构造的系统不满足 Brockett 必要可镇定条件，因此提出设计带有振荡分量的时变反馈控制器。证明了这些控制器能够保证解指数收敛到平凡平衡点，并给出仿真结果以说明闭环系统的行为。
英文摘要：
We consider a kinematic model of a controlled car with two trailers by assuming that each trailer is attached at some distance from the preceding axle ("off-hooked trailers"). For this model, we derive the transformation towards privileged coordinates and present the corresponding nilpotent quasihomogeneous approximate system. The components of this nilpotent approximation are written explicitly in terms of mechanical parameters of the original system. The constructed system does not satisfy the Brockett necessary stabilizability condition, and the design of time-varying feedback controllers with oscillating components is proposed. It is proved that these controllers ensure the exponential convergence of solutions to the trivial equilibrium, and simulation results are presented to illustrate the behavior of the closed-loop system.
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