Constrained LQR Using Online Decomposition Techniques

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.Comment: This technical report is an extended version of the paper titled "Constrained LQR Using Online Decomposition Techniques" submitted to the 2016 Conference on Decision and Contro

Multi-GPU Graph Analytics

We present a single-node, multi-GPU programmable graph processing library that allows programmers to easily extend single-GPU graph algorithms to achieve scalable performance on large graphs with billions of edges. Directly using the single-GPU implementations, our design only requires programmers to specify a few algorithm-dependent concerns, hiding most multi-GPU related implementation details. We analyze the theoretical and practical limits to scalability in the context of varying graph primitives and datasets. We describe several optimizations, such as direction optimizing traversal, and a just-enough memory allocation scheme, for better performance and smaller memory consumption. Compared to previous work, we achieve best-of-class performance across operations and datasets, including excellent strong and weak scalability on most primitives as we increase the number of GPUs in the system.Comment: 12 pages. Final version submitted to IPDPS 201

Distributed Correlation-Based Feature Selection in Spark

CFS (Correlation-Based Feature Selection) is an FS algorithm that has been successfully applied to classification problems in many domains. We describe Distributed CFS (DiCFS) as a completely redesigned, scalable, parallel and distributed version of the CFS algorithm, capable of dealing with the large volumes of data typical of big data applications. Two versions of the algorithm were implemented and compared using the Apache Spark cluster computing model, currently gaining popularity due to its much faster processing times than Hadoop's MapReduce model. We tested our algorithms on four publicly available datasets, each consisting of a large number of instances and two also consisting of a large number of features. The results show that our algorithms were superior in terms of both time-efficiency and scalability. In leveraging a computer cluster, they were able to handle larger datasets than the non-distributed WEKA version while maintaining the quality of the results, i.e., exactly the same features were returned by our algorithms when compared to the original algorithm available in WEKA.Comment: 25 pages, 5 figure

Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path fair resource allocation problem in a distributed SDN control architecture. Our ADMM-based algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances at scale

Towards a cyber physical system for personalised and automatic OSA treatment

Obstructive sleep apnea (OSA) is a breathing disorder that takes place in the course of the sleep and is produced by a complete or a partial obstruction of the upper airway that manifests itself as frequent breathing stops and starts during the sleep. The real-time evaluation of whether or not a patient is undergoing OSA episode is a very important task in medicine in many scenarios, as for example for making instantaneous pressure adjustments that should take place when Automatic Positive Airway Pressure (APAP) devices are used during the treatment of OSA. In this paper the design of a possible Cyber Physical System (CPS) suited to real-time monitoring of OSA is described, and its software architecture and possible hardware sensing components are detailed. It should be emphasized here that this paper does not deal with a full CPS, rather with a software part of it under a set of assumptions on the environment. The paper also reports some preliminary experiments about the cognitive and learning capabilities of the designed CPS involving its use on a publicly available sleep apnea database