Distributed Interior-point Method for Loosely Coupled Problems

In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that combine the Newton and interior-point methods with proximal splitting methods for solving such problems. Particularly, the algorithm for solving unconstrained loosely coupled problems, is based on Newton's method and utilizes proximal splitting to distribute the computations for calculating the Newton step at each iteration. A combination of this algorithm and the interior-point method is then used to introduce a distributed algorithm for solving constrained loosely coupled problems. We also provide guidelines on how to implement the proposed methods efficiently and briefly discuss the properties of the resulting solutions.Comment: Submitted to the 19th IFAC World Congress 201

Geometric Discord Of the Jaynes-Cummings Model: Pure Dephasing Regime

In this paper, the dynamical behaviour of the geometric discord of a system consisting of a two-level atom interacting with a quantised radiation field described by the Jaynes-Cummings model has been studied. The evolution of the system has been considered in the pure dephasing regime when the field is initially in a general pure state and the atom is initially in a mixed state. Dynamics of the geometric discord, as a measure of non-classical correlation, has been compared with the dynamics of negativity, as a measure of quantum entanglement. In particular, the influence of different parameters of system such as detuning and mixedness of the initial atomic state on the dynamics of geometric discord has been evaluated for when the field is initially in coherent and number states. It is shown that for asymptotically large times, the steady state geometric discord of the system presents a non-zero optimum value at some intermediate value of detuning.Comment: 21 pages, 7 figures. appears in Eur. Phys. J. D 201

Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition

Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.Comment: 3 figures. Submitted to the 19th IFAC world congres

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.Comment: Provisionally accepted to appear in IEEE Transactions on Automatic Contro

Distributed Robust Stability Analysis of Interconnected Uncertain Systems

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.Comment: This paper has been accepted for presentation at the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 201