This paper 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 (SOCP). 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.
翻译:本文侧重于在满足安全限制的同时在网上学习系统动态模型。 我们的目标是避免离线系统识别或手指定的模型,并允许一个系统在运行期间安全自主地估计和调整自己的模型。 根据系统状态的不断观测,我们利用巴伊西亚学习获得系统动态的分布。 具体地说,我们建议采用新的矩阵变式高萨进程(MVGP)回归法,并采用高效的共变系数,学习非线性控制-芬菲系统的漂移和输入增益条件。 然后,MVGP分布被用于优化系统行为并确保高度概率的安全,具体指定控制 Lyapunov 函数和控制屏障功能(CBF) 。 我们表明,可以通过解决第二个调控调程序(SOP),将安全控制政策综合到任意相对和具有概率性的系统。 最后,我们把设计扩大到自触发式配制,适应性地决定需要应用新的控制输入的时间,以保证安全。