AI 中文总结
针对含参数不确定性的非线性控制仿射系统，提出鲁棒自适应备份控制障碍函数。用按元素认证的自适应估计器估计未知参数，计算备份流并收紧安全条件，还用基于对偶性的重新表述处理驱动矩阵不确定性，证明该方法能保证系统在相关情况下的安全性。
AI 中文摘要
我们为在漂移动力学和驱动矩阵中都存在参数不确定性的非线性控制仿射系统提出了一种鲁棒自适应备份控制障碍函数的概念。备份控制障碍函数通过在预先认证的安全控制器下预测系统轨迹来保证安全性。然而，这些预测依赖于模型，当系统包含未知参数时可能不准确。为解决此问题，我们使用按元素认证的自适应估计器估计未知参数，该估计器提供参数自适应律和逐分量估计误差界。我们使用估计模型计算备份流，并利用这些认证界收紧安全条件。所得安全条件考虑了预测流对参数估计误差的敏感性。此外，为处理驱动矩阵中的不确定性，我们使用基于对偶性的重新表述，从而能够使用计算效率高的基于二次规划的安全滤波器。我们证明，满足所提出的鲁棒自适应备份控制障碍函数约束的控制器在参数不确定性和输入约束下保证安全性。
英文摘要
We propose a notion of robust adaptive backup control barrier functions for nonlinear control affine systems with parametric uncertainty in both the drift dynamics and actuation matrix. Backup control barrier functions guarantee safety by predicting the system's trajectory under a pre-certified safe controller. However, these predictions rely on the model and can be inaccurate when the system contains unknown parameters. To address this issue, we estimate the unknown parameters using element-wise certified adaptive estimators that provide a parameter adaptation law and component-wise estimation error bounds. We compute the backup flow using the estimated model and tighten the safety conditions using these certified bounds. The resulting safety conditions account for the sensitivity of the predicted flow to parameter estimation errors. Moreover, to handle uncertainty in the actuation matrix, we use a duality-based reformulation that enables the use of a computationally efficient quadratic-program-based safety filter. We prove that controllers satisfying the proposed robust adaptive backup control barrier function constraints guarantee safety under parametric uncertainty and input constraints.
