Feasibility-Guided Learning for Robust Control in Constrained Optimal Control Problems
Feasibility-Guided Learning for Robust Control in Constrained Optimal Control Problems
复制标题
约束最优控制问题中鲁棒控制的可行性引导学习
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
C. Cassandras
中科院分区：
文献类型：
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作者：
Wei Xiao;C. Belta;C. Cassandras
通过使用控制障碍函数（CBF）和控制李雅普诺夫函数（CLF），可以将具有保证安全性和收敛到期望状态的约束的最优控制问题映射为一系列真实的时间优化问题。在这些方法中的主要挑战之一是确保所得到的二次规划（QP）的可行性，如果系统是仿射控制。最近提出的惩罚方法有可能改善这类问题的可行解的存在性。在本文中，我们进一步提高了可行性鲁棒性（即，在存在时变和未知的不安全集的情况下的可行性维护），通过定义适用于任意相对度约束的高阶CBF（HOCBF）;这是通过提出的可行性指导学习方法实现的。具体来说，我们应用机器学习技术，将HOCBF的参数空间分为可行集和不可行集，并得到一个可微分类器，然后将其添加到学习过程中。所提出的可行性指导的学习方法进行了比较与梯度下降法的机器人控制问题。仿真结果表明，改进的能力的可行性指导的学习方法的梯度下降的方法，以确定最佳参数的可行性鲁棒性的HOCBF的定义，以及显示的CBF方法在未知环境中的机器人安全导航的潜力。
Optimal control problems with constraints ensuring safety and convergence to desired states can be mapped onto a sequence of real time optimization problems through the use of Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in these approaches is ensuring the feasibility of the resulting quadratic programs (QPs) if the system is affine in controls. The recently proposed penalty method has the potential to improve the existence of feasible solutions to such problems. In this paper, we further improve the feasibility robustness (i.e., feasibility maintenance in the presence of time-varying and unknown unsafe sets) through the definition of a High Order CBF (HOCBF) that works for arbitrary relative degree constraints; this is achieved by a proposed feasibility-guided learning approach. Specifically, we apply machine learning techniques to classify the parameter space of a HOCBF into feasible and infeasible sets, and get a differentiable classifier that is then added to the learning process. The proposed feasibility-guided learning approach is compared with the gradient-descent method on a robot control problem. The simulation results show an improved ability of the feasibility-guided learning approach over the gradient-decent method to determine the optimal parameters in the definition of a HOCBF for the feasibility robustness, as well as show the potential of the CBF method for robot safe navigation in an unknown environment.