Tube-Based Model Predictive Control Using Multidimensional Taylor Network for Nonlinear Time-Delay Systems

For nonlinear time-delay systems with uncertainties, the existing approaches to robust model predictive control (MPC) are based on the min-max optimization formulation. Unfortunately, these approaches are generally conservative for most practical problems. For this sake, this article proposes a tube-based MPC consisting of MPC and control contraction metric (CCM) controller. The MPC is utilized as a nominal controller to generate a reference trajectory, while the CCM controller is used as a local ancillary controller to guarantee the actual trajectory to be contained within a robust invariant tube centered along the reference trajectory. Besides, we construct a variational formulation multidimensional Taylor network (MTN) as the basis function to search for the minimal geodesic. With the effective training algorithm, MTN could efficiently approximate the solution with high accuracy. The incremental exponential stability of the considered systems is proved theoretically, and the effectiveness of the proposed method is illustrated by numerical simulation.