Safe Control Design for Unknown Nonlinear Systems with Koopman-based Fixed-Time Identification

• Main Authors: Black, Mitchell, Panagou, Dimitra
• Format: Journal Article
• Language: English
• Published: 01.12.2022
• Subjects: Computer Science - Systems and Control; Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.2212.00624

We consider the problem of safe control design for a class of nonlinear, control-affine systems subject to an unknown, additive, nonlinear disturbance. Leveraging recent advancements in the application of Koopman operator theory to the field of system identification and control, we introduce a novel fixed-time identification scheme for the infinitesimal generator of the infinite-dimensional, but notably linear, Koopman dynamical system analogous to the nonlinear system of interest. That is, we derive a parameter adaptation law that allows us to recover the unknown, residual nonlinear dynamics in the system within a finite-time independent of an initial estimate. We then use properties of fixed-time stability to derive an error bound on the residual vector field estimation error as an explicit function of time, which allows us to synthesize a provably safe controller using control barrier function based methods. We conduct a quadrotor-inspired case study in support of our proposed method, in which we show that safe trajectory tracking is achieved despite unknown, nonlinear dynamics.