Stability conditions for linear time-varying model predictive control in autonomous driving
Stability conditions for linear time-varying model predictive control in autonomous driving
复制标题
自动驾驶中线性时变模型预测控制的稳定性条件
DOI：
10.1109/cdc.2017.8264062
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
B. Wahlberg
中科院分区：
文献类型：
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作者：
P. Lima;J. Mårtensson;B. Wahlberg
本文提出了稳定性条件时，设计的线性时变模型预测控制器的横向控制的自主车辆。通过添加终端状态约束和终端成本，通过李雅普诺夫技术证明了稳定性。我们详细介绍了如何计算线性时变情况下的终端状态和终端成本，并解释了自动驾驶应用程序的光所获得的结果。为了确定稳定性条件，使用多模型描述的概念，其中线性时变模型被分离成依赖于单个参数的有限数量的时不变模型。终端集是多模型描述的最大正不变集，并且终端成本是最小-最大优化的结果，该最小-最大优化确定最差的时不变模型（如果用作预测模型）。事实上，在自动驾驶的情况下，我们证明了最小-最大方法是一个凸优化问题。离线计算的稳定性条件，保持凸性的优化，并不影响控制器的执行时间。在仿真中，我们证明了稳定的有效性，所提出的条件，通过一个说明性的例子，与重型车辆的路径跟踪。
This paper presents stability conditions when designing a linear time-varying model predictive controller for lateral control of an autonomous vehicle. Stability is proved via Lyapunov techniques by adding a terminal state constraint and a terminal cost. We detail how to compute the terminal state and the terminal cost for the linear time-varying case, and interpret the obtained results in the light of an autonomous driving application. To determine the stability conditions, the concept of multi-model description is used, where the linear time-varying model is separated into a finite number of time-invariant models that depend on a single parameter. The terminal set is the maximum positive invariant set of the multi-model description and the terminal cost is the result of a min-max optimization that determines the worst time-invariant model if used as a prediction model. In fact, in the autonomous driving case, we show that the min-max approach is a convex optimization problem. The stability conditions are computed offline, maintain the convexity of the optimization, and do not affect the execution time of the controller. In simulation, we demonstrate the stabilizing effectiveness of the proposed conditions through an illustrative example of path following with a heavy-duty vehicle.