Control Lyapunov-Barrier function-based predictive control using a deep hybrid model with guarantees on domain of applicability

The domain of applicability (DA) of a data-driven model is limited by its training data. Consequently, the DA of a hybrid model which combines a first-principles model with a data-driven model is also limited by its training data even though it has better extrapolation capabilities compared to a data-based model. Nonetheless, the domain of applicability (DA) of a hybrid model is finite and should be taken into account when developing a hybrid model-based predictive controller in order to maximize its performance. To this end, a Control Lyapunov-Barrier Function-based model predictive controller (CLBF-based MPC) is developed which utilizes a deep hybrid model (DHM), i.e., a deep neural network (DNN) combined with a first-principles model. Additionally, theoretical guarantees are provided on stability as well as on system states to stay within the DA of the DHM. The efficacy of the proposed framework is demonstrated on a continuous stirred tank reactor.