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Large-scale industrial processes usually adopt centralized control and optimization methods. However, with the growth of the scale of industrial processes leading to increasing computational complexity, the online optimization capability of the double-layer model predictive control algorithm is challenged, exacerbating the difficulty of the widespread implementation of this algorithm in the industry. This paper proposes a distributed double-layer model predictive control algorithm based on dual decomposition for multivariate constrained systems to reduce the computational complexity of process control. Firstly, to solve the problem that the original dual decomposition method does not apply to constrained systems, two improved dual decomposition model prediction control methods are proposed: the dual decomposition method based on the quadratic programming in the subsystem and the dual decomposition method based on constraint zones, respectively. It is proved that the latter will certainly converge to the constraint boundaries with appropriate convergence factors for the controlled variables. The online optimization ability of the proposed two methods is compared in discussion and simulation, concluding that the dual decomposition method based on the constraint zones exhibits superior online optimization ability. Further, a distributed double-layer model predictive control algorithm with dual decomposition based on constraint zones is proposed. Different from the objective function of the original dual decomposition model predictive control, the proposed algorithm's dynamic control-layer objective function simultaneously tracks the steady-state optimization values of the controlled and manipulated variables, giving the optimal solution formulation of the optimization problem consisting of this objective function and the constraints. The algorithm proposed in this paper achieves the control goals while significantly reducing the computational complexity and has research significance for promoting the industrial implementation of double-layer model predictive control. [ABSTRACT FROM AUTHOR]

Ordinal regression methods are widely used to predict the ordered labels of data, among which support vector ordinal regression (SVOR) methods are popular because of their good generalization. In many realistic circumstances, data are collected by a distributed network. In order to protect privacy or due to some practical constraints, data cannot be transmitted to a center for processing. However, as far as we know, existing SVOR methods are all centralized. In the above situations, centralized methods are inapplicable, and distributed methods are more suitable choices. In this paper, we propose a distributed SVOR (dSVOR) algorithm. First, we formulate a constrained optimization problem for SVOR in distributed circumstances. Since there are some difficulties in solving the problem with classical methods, we used the random approximation method and the hinge loss function to transform the problem into a convex optimization problem with constraints. Then, we propose subgradient-based algorithm dSVOR to solve it. To illustrate the effectiveness, we theoretically analyze the consensus and convergence of the proposed method, and conduct experiments on both synthetic data and a real-world example. The experimental results show that the proposed dSVOR could achieve close performance to that of the corresponding centralized method, which needs all the data to be collected together. [ABSTRACT FROM AUTHOR]