Understand
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.