Transferring Controller from Math to Real World Systems: A Formal Control Theoretic Approach

Abstract

The letter aims to improve the math-to-real or math-to-sim transfer of a mission controller designed for a Temporal Reach Avoid Stay (T-RAS) specification. Our approach uses the control-theoretic concept of Incremental Input-to-State stability ($δ$-ISS). We model the real-world system as an uncertain system, represented by a nominal mathematical model with an additive disturbance. Our method involves two steps: firstly, we make the nominal mathematical model and the real-world system $δ$-ISS. Secondly, we design a mission controller for the mathematical model that satisfies a modified specification. We then prove that applying the same mission-level input sequence to the real-world system guarantees that the original specification is satisfied in the real world. Videos of real-world experiments are available at https://youtu.be/NvjkIZxtnPM.