Control Barriers in Bayesian Learning of System Dynamics
Control Barriers in Bayesian Learning of System Dynamics
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DOI：
10.1109/tac.2021.3137059
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发表时间：
2020-12
影响因子：
6.8
通讯作者：
Vikas Dhiman;M. J. Khojasteh;M. Franceschetti;Nikolay A. Atanasov
中科院分区：
文献类型：
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作者：
Vikas Dhiman;M. J. Khojasteh;M. Franceschetti;Nikolay A. Atanasov
本文的重点是在线学习系统动力学模型，同时满足安全约束。我们的目标是避免离线系统识别或手动指定模型，并允许系统在运行期间安全地、自主地估计和调整自己的模型。在给定系统状态的流观测的情况下，我们使用贝叶斯学习来获得系统动态的分布。具体地说，我们提出了一种新的矩阵变量高斯过程(MVGP)回归方法，利用有效的协方差分解来学习非线性控制-仿射系统的漂移项和输入增益项。通过指定控制李雅普诺夫函数(CLF)和控制屏障函数(CBF)机会约束，利用MVGP分布优化系统行为，以高概率保证系统安全。我们证明了对于具有任意相对度和概率CLF-CBF约束的系统，可以通过求解一个二阶锥规划来综合安全控制策略。最后，我们将我们的设计扩展到自触发公式，自适应地确定需要应用新的控制输入以确保安全的时间。
This article focuses on learning a model of system dynamics online, while satisfying safety constraints. Our objective is to avoid offline system identification or hand-specified models and allow a system to safely and autonomously estimate and adapt its own model during operation. Given streaming observations of the system state, we use Bayesian learning to obtain a distribution over the system dynamics. Specifically, we propose a new matrix variate Gaussian process (MVGP) regression approach with an efficient covariance factorization to learn the drift and input gain terms of a nonlinear control-affine system. The MVGP distribution is then used to optimize the system behavior and ensure safety with high probability, by specifying control Lyapunov function (CLF) and control barrier function (CBF) chance constraints. We show that a safe control policy can be synthesized for systems with arbitrary relative degree and probabilistic CLF-CBF constraints by solving a second-order cone program. Finally, we extend our design to a self-triggering formulation, adaptively determining the time at which a new control input needs to be applied in order to guarantee safety.