Safety constraints of nonlinear control systems are commonly enforced through the use of control barrier functions (CBFs). By defining the boundary of a set of safe states using CBFs, a set of safety-ensuring control inputs can be found. Each of these control inputs in this set renders the safe set of states forward invariant, meaning that trajectories that begin inside the safe set stay there for all time. Unlike in constructive Lyapunov-based methods, where a system's control input is designed to drive the state to a desired equilibrium point, CBFs allow the synthesis of pointwise-optimal controllers (often in the form of quadratic programs) that make a selection from the set of safe control inputs that minimizes some cost function. In this talk, I will present two approaches for overcoming common limitations in CBF works. The first is high-order CBFs (HOCBFs), which help to extend CBF methods to systems of higher relative degrees, allowing for broader application to systems with complex dynamics. While the developed HOCBF method is applicable to a variety of nonlinear systems, the effectiveness of the developed approach is demonstrated on a motorized rehabilitative cycling system of relative degree two. Second, to address potential uncertainties in the dynamic model, which can disrupt forward invariance guarantees, I will present on adaptive deep neural network (DNN)-based CBFs. The combination of adaptive DNNs and CBFs ensures safety while the system's dynamics are learned in real-time, without the need for pre-training. A Lyapunov-based analysis yields guarantees on the DNN parameter estimation error, unlike in previous results. Comparative simulations are presented to demonstrate the performance of the developed method on two control systems, including the potential for use during intermittent loss of state feedback.

Host: Anatoly Zlotnik (T-5)