Conformant Synthesis for Koopman Operator Linearized Control Systems

One very promising approach for controlling nonlinear systems is Koopman operator linearization, which approximates nonlinear dynamics with a higher-dimensional linear system. However, since the resulting Koopman linearized model only estimates the actual dynamics, one cannot provide any safety guarantees for the resulting controllers. In this paper we propose a solution to the safety-issue by constructing a Koopman linearized model that is conformant with measurements from the real system using a novel conformant synthesis algorithm that combines trace conformance and reachset conformance. The resulting conformant model can then be used to construct controllers that are safe despite process noise and measurements errors acting on the real system. We demonstrate the superior performance of our conformant synthesis approach compared to previous methods using real data from an electric circuit and a robot manipulator, and we apply our overall framework to safely control a F1tenth racecar.