Data-driven Safe Control for Nonlinear Systems

Presented as part of the 2018 HCSS conference.

ABSTRACT

Data-driven methods based on machine learning have been adopted to runtime design and optimization of the control of autonomous cyber-physical systems. These methods exploit previous experience of a system to achieve high performance but they lack safety guarantees. Thus, their adoption in safety-critical systems often requires a simplex architecture with a backup model-based safety controller that guarantees the system's safety while data-driven controller optimizes performance within the safety envelope. But the absence of reasonably accurate but yet tractable models poses a major challenge. In this paper, we present a novel data-driven approach for the synthesis of this backup safety controller. Our method requires only an approximate linear model of the system and Lipschitz continuity of the unknown nonlinear dynamics. The nonlinear dynamics is conservatively modeled as a quadratic state-dependent disturbance of a base linear system and this quadratic disturbance is learned from data. The synthesis of the safety controller and the safe set is then performed by restricting the safe set to be elliptical and using a quadratic Lyapunov function as safety certificate.  We experimentally demonstrate the effectiveness of the proposed approach.