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 paper proposes a tubebased 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 multi-dimensional 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.

For non‐linear control, it is important to secure a generally structured controller that promises wide application and desirable performance. This study deals with the problem of asymptotic tracking and dynamic regulation of single‐input single output (SISO) non‐linear systems via output feedbacks by the discrete multi‐dimensional Taylor network (MTN) controller, a novel controller with fixed structure and sampled‐data control mechanism. For verification of its validity, differential geometry and polynomial approximation are adopted. Using the emulation technique and regional pole assignment, the asymptotic tracking and dynamic regulation without online optimisation of the system by discrete MTN controller is tested. With the dynamic change of error signals, the dynamic regulation by given index is realised. As a convex optimisation problem, the controller parameters can be acquired by parametric learning. Based on the delta operator model, the procedure of the controller design is given in detail. Simulation results confirm the feasibility and effectiveness of the proposed approach.

In this study, the problem of adaptive multi‐dimensional Taylor network (MTN) control for single‐input single‐output (SISO) uncertain stochastic non‐linear systems is investigated. How to minimise the influence of randomness and uncertain non‐linearity for less complex computation, and how to improve the real‐time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non‐linear systems. MTNs are used to approximate the non‐linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real‐time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real‐time performance and control quality.

We address the closely related problems of production planning and scheduling on mixed model automobile assembly lines. We propose an integrated solution, in which a production plan that is feasible with respect to aggregate capacity constraints is developed and then a sequence that is feasible with respect to this plan is sought. We propose three tabu-search-based algorithms that explore the solution spaces for both problems to different degrees to find a combination of a production plan and schedule that are feasible and that approximately optimize the objective function (involving the overproduction and underproduction of finished automobiles, the set-up cost, the idle times of work-cells on the line, the makespan and the load deviations among work-cells). Simulation is used to evaluate alternative schedules. Stochastic extensions are proposed and the complexities of these algorithms are discussed. Example runs comparing the algorithms are presented for deterministic cases, stochastic cases, types of automobiles, buffer sizes and number of work-cells. The results show that an embedded tabu search algorithm is suitable for solving small scale problems, an alternate tabu search algorithm for the medium scale and a serial tabu search algorithm for the large scale.