Learning-enabled stochastic predictive control for nonlinear discrete-time step backward high-order fully actuated systems

In this paper, we seamlessly integrate machine learning techniques with stochastic Model Predictive Control (MPC) to address the regulation problem of nonlinear discrete-time step backward High-Order Fully Actuated (HOFA) systems with additive disturbance. By exploiting the full-actuation characteristic of the HOFA system, we neatly eliminate the non-linearity of the system, thus circumventing the complex computation of uncertainty propagation in nonlinear stochastic MPC. To cope with the random disturbance, its probability distribution on each principal component is well captured from data based on principal component analysis, and the uncertainty bound is effectively estimated via kernel density estimation and quantile functions. Based upon such probabilistic information, we impose constraint tightening on the state limits and define terminal sets by drawing on the concept of tubes. On this basis, we employ stochastic MPC for receding horizon control of HOFA systems, of which the recursive feasibility and stability are proved theoretically. Finally, numerical experiments and an application to hydrogen electrolyzer temperature control are used to demonstrate the merits of the proposed approach in comparison with state-of-the-art methods.