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We address the optimal dynamic formation problem in mobile leader-follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem. When the optimal formation objective is to maximize coverage in a mission space cluttered with obstacles, we separate the process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process.

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm., Accepted to IEEE Conference on Decision and Control (CDC) 2015

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received much attention lately. In particular, linear convergence rates have been shown by several authors under various assumptions. One such set of assumptions is strong convexity and smoothness of one of the functions in the minimization problem. The authors recently provided a linear convergence rate bound for such problems. In this paper, we show that this rate bound is tight for the class of problems under consideration.

A new challenge for learning algorithms in cyber-physical network systems is the distributed solution of big-data classification problems, i.e., problems in which both the number of training samples and their dimension is high. Motivated by several problem set-ups in Machine Learning, in this paper we consider a special class of quadratic optimization problems involving a "large" number of input data, whose dimension is "big". To solve these quadratic optimization problems over peer-to-peer networks, we propose an asynchronous, distributed algorithm that scales with both the number and the dimension of the input data (training samples in the classification problem). The proposed distributed optimization algorithm relies on the notion of "core-set" which is used in geometric optimization to approximate the value function associated to a given set of points with a smaller subset of points. By computing local core-sets on a smaller version of the global problem and exchanging them with neighbors, the nodes reach consensus on a set of active constraints representing an approximate solution for the global quadratic program.

We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimization problems are approximated using the Legendre-Gauss-Lobatto (LGL) pseudospectral collocation scheme to yield a family of nonlinear programs, whose solutions approach the optima with finer discretization. Simulation and optimization of time-varying scenarios on an example natural gas transmission network demonstrate the gains in security and efficiency over methods that assume steady-state behavior.