Summary: This article is concerned with the problem of robust model predictive control (MPC) for uncertain nonlinear time-delay systems. In order to reduce the computational conservativeness of the existing robust MPC given in the min-max optimization formulation, a novel tube-based MPC method is investigated via exploring MPC and control contraction metric (CCM) technique. Based on the Lyapunov-Krasovskii arguments, the MPC is designed as a nominal controller to generate a reference trajectory. By constructing a functional formulation of the inner product on tangent space, the CCM technique is applied to develop a local ancillary controller to guarantee the actual trajectory being contained within a robust invariant tube. In addition, to alleviate the burden of computing geodesic in the design of CCM technique, we propose a direct method using the neural network to search for the minimal geodesic online. By employing the sequential quadratic programming algorithm, this method improves the efficiency of online calculation with high accuracy. Finally, numerical simulation is employed to validate the effectiveness of the proposed method.
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