Safe and Stable Adaptive Control for a Class of Dynamic Systems

Abstract: Adaptive control has focused on online control of dynamic systems in the presence of parametric uncertainties, with solutions guaranteeing stability and control performance. Safety, a related property to stability, is becoming increasingly important as the footprint of autonomous systems grows in society. One of the popular ways for ensuring safety is through the notion of a control barrier function (CBF). In this paper, we combine adaptation and CBFs to develop a real-time controller that guarantees stability and remains safe in the presence of parametric uncertainties. The class of dynamic systems that we focus on is linear time-invariant systems whose states are accessible and where the inputs are subject to a magnitude limit. Conditions of stability, state convergence to a desired value, and parameter learning are all elucidated. One of the elements of the proposed adaptive controller that ensures stability and safety is the use of a CBF-based safety filter that suitably generates safe reference commands, employs error-based relaxation (EBR) of Nagumo's theorem, and leads to guarantees of set invariance. To demonstrate the effectiveness of our approach, we present two numerical examples, an obstacle avoidance case and a missile flight control case.