quadratic optimization problems appear in several interesting estimation, learning and control tasks. To solve these problems in peer-to-peer networks it is necessary to design distributed optimization algorithms supp...
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(纸本)9783952426937
quadratic optimization problems appear in several interesting estimation, learning and control tasks. To solve these problems in peer-to-peer networks it is necessary to design distributed optimization algorithms supporting directed, asynchronous and unreliable communication. This paper addresses this requirement by extending a promising distributed convex optimization algorithm, known as Newton-Raphson consensus, and originally designed for static and undirected communication. Specifically, we modify this algorithm so that it can cope with asynchronous, broadcast and unreliable lossy links, and prove that the optimization strategy correctly converge to the global optimum when the local cost functions are quadratic. We then support the intuition that this robustified algorithm converges to the true optimum also for general convex problems with dedicated numerical simulations.
In this study, the solution of a convex distributed optimisation problem with a global coupling inequality constraint is considered. By using the Lagrange duality framework, the problem is transformed into a distribut...
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In this study, the solution of a convex distributed optimisation problem with a global coupling inequality constraint is considered. By using the Lagrange duality framework, the problem is transformed into a distributed consensus optimisation problem and then based on the recently proposed Hybrid Alternating Direction Method of Multipliers (H-ADMM), which merges distributed and centralised optimisation concepts problems, a novel distributed algorithm is developed. In particular, the authors offer a reformulation of the original H-ADMM in an operator theoretical framework, which exploits the known relationship between ADMM and Douglas-Rachford splitting. In addition, the authors' formulation allows us to generalise the H-ADMM by including a relaxation constant, not present in the original design of the algorithm. Moreover, an adaptive penalty parameter selection scheme that consistently improves the practical convergence properties of the algorithm is proposed. Finally, the convergence results of the proposed algorithm are discussed and moreover, in order to present the effectiveness and the major capabilities of the proposed algorithm in off-line and on-line scenarios, distributed quadratic programming and distributed model predictive control problems are considered in the simulation section.
This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth...
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This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth, owing to the broad applicability of the switched system framework. For example, the switched system can be adopted for modeling the dynamics of numerous systems including power systems, manufacturing systems, aerospace systems, networked control systems, etc. Despite considerable research works that have been developed during last several decades, there are still remaining yet important and unsolved problems for the switched systems. In the first part of this dissertation, new methods are developed for uncertainty propagation of stochastic switched systems in the presence of the state uncertainty, represented by probability density functions(PDFs). The main difficulty of this problem is that the number of PDF components in the state increases exponentially under the stochastic switching, incurring the curse of dimensionality. This dissertation provides a novel method that circumvents the issue regarding the curse of dimensionality. As an extension of this research, the new method for the switching synthesis is presented in the second part, to achieve the optimal performance of the switched system. This research is relevant to developing the switching synthesis on how to switch between different switching modes. In the following chapters, some interesting applications that emerges as today's leading-edge technology in high-performance computing (HPC) will be introduced. Generally, the massive parallel computing entails idle process time in multi-core processors or distributed computing devices as up to 80% of total computation time, owing to the synchronization of the data. Thus, there is a trend toward relaxing such a restriction on synchronization penalty to overcome this bottleneck problem. This dissertation presents a synchronous computing algorith
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