High-Confidence Barrier-Certified Control Design Using Goal-Oriented Scenario Optimization and Experience Replay Model Learning

This paper presents a probabilistic framework to design safe controllers for linear systems under parametric uncertainties. To this end, a two-layer learning-enabled controller is presented that unifies the experience-replay model learning and the scenario-based optimization. The inner loop leverages the scenario optimization to impose probabilistic stability and safety specifications through sampling from a control Lyapunov function and a control barrier function, respectively. Each sample represents a plausible system dynamics realization within the range of the uncertainties. To quantify the model uncertainty and, thus, to facilitate a proactive and goal-oriented sampling of safety and stability constraints, an experience replay-based model learning is presented in the outer loop. The exponentially fast convergent guarantees of the presented approach and the quantification of the exponential rate using the collected data allow us to quantify the ambiguity set for the system parameters based on the data informativeness. The quantified modeling error acts as a vanishing perturbation to the true dynamics, from which samples can be taken at a specific frequency to solve an optimization problem in the inner loop. The presented approach provides safety and stability guarantees with high probability, even during learning. Simulation is used to depict the efficacy of the proposed approach.