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In this paper, we examine the problems of existence and computation of proper and stable stabilising compensators in the feedback path of a special class of linear time-invariant multivariable systems characterised by a strictly proper transfer function matrix. For the class of systems that are 'square', i.e. have the same number of inputs and outputs and have no zeros in the closed right half complex plane and the class of 'non-square' systems that include a 'square' subsystem that has no zeros in the closed right half complex plane we present a sufficient condition for the existence and computation of proper stabilising (pole placing) compensators which in certain cases that depend on the transfer function matrix of the system can be chosen to be stable. [ABSTRACT FROM AUTHOR]

Traditional machine learning relies on a centralized data pipeline for model training in various applications; however, data are inherently fragmented. Such a decentralized nature of databases presents the serious challenge for collaboration: sending all decentralized datasets to a central server raises serious privacy concerns. Although there has been a joint effort in tackling such a critical issue by proposing privacy-preserving machine learning frameworks, such as federated learning, most state-of-the-art frameworks are built still in a centralized way, in which a central client is needed for collecting and distributing model information (instead of data itself) from every other client, leading to high communication burden and high vulnerability when there exists a failure at or an attack on the central client. Here we propose a principled decentralized federated learning algorithm (DeceFL), which does not require a central client and relies only on local information transmission between clients and their neighbors, representing a fully decentralized learning framework. It has been further proven that every client reaches the global minimum with zero performance gap and achieves the same convergence rate $O(1/T)$ (where $T$ is the number of iterations in gradient descent) as centralized federated learning when the loss function is smooth and strongly convex. Finally, the proposed algorithm has been applied to a number of applications to illustrate its effectiveness for both convex and nonconvex loss functions, time-invariant and time-varying topologies, as well as IID and Non-IID of datasets, demonstrating its applicability to a wide range of real-world medical and industrial applications.

This article investigates the distributed optimization feedback control for a family of multi‐agent systems with external disturbances. For physical implementation in the scenario that only the sampled‐state information is available, a novel disturbance compensation distributed optimization control strategy is proposed by designing a sampled‐data‐based distributed protocol and a sampled‐data‐based disturbance compensator. The disturbances in the current sampling interval are compensated by an exact value at the time in the last sampling interval obtained by using the sampled data. It is proved that the states of agents converge to an arbitrarily small domain of the optimal point of the global cost function if the disturbances and their derivatives are bounded, and the sampling period is short enough. Besides, when disturbances are constants, all the agents' states converge to the optimal point asymptotically. Simulations consolidated the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Existing work on offline data-driven optimization mainly focuses on problems in static environments, and little attention has been paid to problems in dynamic environments. Offline data-driven optimization in dynamic environments is a challenging problem because the distribution of collected data varies over time, requiring surrogate models and optimal solutions tracking with time. This paper proposes a knowledge-transfer-based data-driven optimization algorithm to address these issues. First, an ensemble learning method is adopted to train surrogate models to leverage the knowledge of data in historical environments as well as adapt to new environments. Specifically, given data in a new environment, a model is constructed with the new data, and the preserved models of historical environments are further trained with the new data. Then, these models are considered to be base learners and combined as an ensemble surrogate model. After that, all base learners and the ensemble surrogate model are simultaneously optimized in a multitask environment for finding optimal solutions for real fitness functions. In this way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the ensemble model is the most accurate surrogate, we assign more individuals to the ensemble surrogate than its base learners. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art offline data-driven optimization algorithms. Code is available at https://github.com/Peacefulyang/DSE_MFS.git. [ABSTRACT FROM AUTHOR]