Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)

A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach implementatio

Control of Unknown Nonlinear Systems with Linear Time-Varying MPC

We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time-varying regions of the state space to construct an Affine Time-Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Controller (MPC) which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used estimation and linearization methods fail