发表机构
Illinois Institute of Technology; Lamar University（伊利诺伊理工学院; 拉玛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于多步高斯过程回归的模型预测控制方法，用于安全控制状态与控制相关的不确定性系统，并通过车辆换道仿真验证了其有效性。
AI 中文摘要
我们提出了一种新颖的模型预测控制方法，该方法结合了多步不确定性预测，用于安全控制那些不确定性同时依赖于状态变量和控制变量的系统。真实系统与其面向控制的表示之间的差异源于固有不确定性，这些不确定性通常与状态变量和控制变量相关，这在建模误差中很常见。随着这些不确定性随时间累积和传播，它们会在较长时间范围内产生显著偏差，可能危及安全关键应用的完整性。尽管现有的随机控制框架能够在指定的置信水平下将系统运行维持在安全边界内，但它们需要在整个控制时域内准确预测状态分布。对于不确定性随状态和控制输入变化的系统，这一预测是一项重大挑战。我们的贡献通过一种利用多步高斯过程回归来捕获和预测状态相关及控制相关不确定性的模型预测控制器来解决这一挑战。我们进一步提出了针对我们MPC框架中优化问题的迭代求解方法，并讨论了算法的收敛性。为了在实际应用中展示该方法，我们对车辆横向控制进行了深入分析，特别是在车道变换操作期间，考察了误差如何通过系统模型传播。我们提出的方法的有效性通过全面的仿真得到了验证。
英文摘要
We introduce a novel approach to model predictive control that incorporates multi-step uncertainty prediction for safely controlling systems characterized by uncertainties dependent on both state and control variables. The discrepancy between real-world systems and their control-oriented representations arises from inherent uncertainties, which frequently correlate with state and control variables, a common occurrence in modeling errors. As these uncertainties accumulate and propagate over time, they can produce substantial deviations over extended horizons, potentially compromising the integrity of safety-critical applications. Although existing stochastic control frameworks can maintain system operation within safety boundaries at specified confidence levels, they necessitate accurate prediction of state distributions throughout the control horizon. This prediction represents a significant challenge for systems where uncertainties vary with state and control inputs. Our contribution addresses this challenge through a Model Predictive Controller leveraging multi-step Gaussian Process Regression to capture and anticipate uncertainties that are state- and control-dependent. We further propose an iterative solution to the optimization problem in our MPC framework and discuss the convergence of the algorithm. To demonstrate the method in a practical application, we conduct an in-depth analysis of vehicle lateral control, particularly during lane-changing maneuvers, examining how errors propagate through the system model. The effectiveness of our proposed methodology is validated through comprehensive simulations.
Comments10 pages, 11 figures
