Fixed-Time Parameter Adaptation for Safe Control Synthesis

Mitchell Black, Ehsan Arabi, and Dimitra Panagou

Submitted to Automatica (under review)

We propose a fixed-time stable parameter adaptation law that guarantees that an additive, parameter-affine disturbance appearing in the dynamics of a class of nonlinear, control-affine systems is learned within a fixed time. We then provide an upper bound on the parameter estimation error as an explicit function of time, and use such knowledge to formulate a control barrier function condition to guarantee safety of the system trajectories at all times. We further show that our proposed parameter adaptation law is robust against bounded perturbations to the system dynamics in that the resulting estimated parametric disturbance converges to a known neighborhood of the true parametric disturbance within a fixed time. To illustrate the advantages of our proposed approach, we conduct a comparative numerical study against various controllers from the literature. Finally, we validate our approach on a trajectory-tracking problem subject to safety requirements using a 6 degree-of-freedom quadrotor model in an unknown wind field.