Control Barriers in Bayesian Learning of System Dynamics
This work is significant for robotic systems and autonomous agents that need to learn and adapt their models online while guaranteeing safety, reducing the reliance on offline identification or hand-specified models.
This paper addresses the problem of online learning of system dynamics while ensuring safety constraints. It proposes a new matrix variate Gaussian process (MVGP) regression approach to learn the drift and input gain terms of a nonlinear control-affine system, enabling the synthesis of a safe control policy by solving a second order cone program (SOCP) with probabilistic CLF-CBF constraints.
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.