We formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.

Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. Unmannned aerial vehicles (UAVs) can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment and collect data therein for long time periods. The enduring nature of these missions requires the UAV to be regularly recharged at a service station. In this article, we consider the case in which the service station is not colocated with any of the targets. An efficient monitoring requires the revisit time, defined as the maximum of the time elapsed between successive revisits to targets, to be minimized. Here, we consider the problem of determining UAV routes that lead to the minimum revisit time. The problem is NP-hard, and its computational difficulty increases with the fuel capacity of the UAV. We develop an algorithm to construct near-optimal solutions to the problem quickly when the fuel capacity exceeds a threshold. We also develop lower bounds to the optimal revisit time and use these bounds to demonstrate (through numerical simulations) that the constructed solutions are, on an average, at most 0.01% away from the optimum.

In this article, we consider a routing problem that arises in the scenario of persistently monitoring a set of targets using an unmanned vehicle. A UAV is tasked with monitoring a set of targets, by frequently visiting them for data collection. The UAV has a limited fuel capacity, which is specified in terms of the number of visits it makes, at the end of which it must be recharged at a depot. The problem considered here is to plan an optimal sequence of visits (to targets) for the UAV, such that the maximum time between consecutive revisits to the targets is minimized. The problem is a generalization of the Traveling Salesman Problem (TSP) and is computationally challenging; It is significantly difficult to compute optimal solutions using standard formulations. However, the authors recently developed a set of theoretical results characterizing the structure of optimal solutions for this problem. Using these results, in this article, we propose a new formulation to solve the problem. Extensive numerical simulations suggest that the average computation time required to solve the problem using the proposed formulation is within a fraction of a second on a standard laptop (here, a MacBook Pro with Intel Core i7 processor and 16 GB RAM was used).