Deep-Neural-Network-Controlled Safety-Critical Systems With Uncertainty Resilience

The rapid developments of machine learning techniques open new viewpoints of control designs for cyber-physical systems, especially for their intrinsical advantages in adaptability to uncertain environment, less conservatism as well as extensible safe region compared to classical control schemes. In this paper, we synthesize the deep neural network (DNN)-based control architecture for safety-critical systems with uncertainty resilience. This can be achieved by deploying a DNN controller to stabilize a class of constrained nonlinear systems with unknown uncertainties and a DNN compensator to estimate the uncertainty impacts on the safety certificates to modify the control actions leading to safety preference. Based on the quadratic constraint of DNN and Lipschitz smoothness of nonlinear plant, we establish the formal guarantees on ensuring the closed-loop stability and obtain the optimal inner approximation of region of attraction. We then develop the DNN-based estimators of uncertainty impacts embedded in discrete-time control barrier functions with different relative of degrees via imitation learning, respectively, such that the control inputs can be minimally modified by the learning-based safety filter to realize the collision avoidance. The applicability of our theoretical results is demonstrated by the case study of vehicle lateral dynamics.