  Safety and tracking stability are crucial for safety-critical systems such as
self-driving cars, autonomous mobile robots, industrial manipulators. To
efficiently control safety-critical systems to ensure their safety and achieve
tracking stability, accurate system dynamic models are usually required.
However, accurate system models are not always available in practice. In this
paper, a learning-based safety-stability-driven control (LBSC) algorithm is
presented to guarantee the safety and tracking stability for nonlinear
safety-critical systems subject to control input constraints under model
uncertainties. Gaussian Processes (GPs) are employed to learn the model error
between the nominal model and the actual system dynamics, and the estimated
mean and variance of the model error are used to quantify a high-confidence
uncertainty bound. Using this estimated uncertainty bound, a safety barrier
constraint is devised to ensure safety, and a stability constraint is developed
to achieve rapid and accurate tracking. Then the proposed LBSC method is
formulated as a quadratic program incorporating the safety barrier, the
stability constraint, and the control constraints. The effectiveness of the
LBSC method is illustrated on the safety-critical connected cruise control
(CCC) system simulator under model uncertainties.
