Degree design of coupled infrastructures

A recent asymptotic model of cascading failure in two-domain, coupled infrastructures is used to pose and solve a specific degree-distribution design problem. Low-order non-linear analysis exposes the mechanisms by which optimised graphs can form star-like clusters, and suggests why the optimisation is well-behaved numerically. Through computational examples on coupled systems of finite size, we demonstrate that the model assumption of degree independence can be somewhat relaxed, which is significant for geometric connectivity. Further, an assortative heuristic rule that matches degrees across the domain boundary can offer benefits in most finite-size cases

Linearized Hovering Control With One or More Azimuthing Thrusters

We propose a simple method of control system design for marine vehicles with one or more azimuthing propulsors, and specifically for the case where the speed of the actuator is on the same time scale as the plant dynamic response, thus making the assumption of a separation of time scales invalid. By setting a fixed, regular azimuth trajectory, the control problem is simplified sufficiently to allow a fully linear design approach, for which bandwidth achieved, robustness, and disturbance and noise rejection, will be more tangible than in the nonlinear cases. Several simulation examples are presented for a new vehicle that is in development; the approach would apply directly to the cases of multiple propulsors and dynamic positioning as well.United States. Office of Naval Research (Grant N00014-02-C-0202); United States. National Oceanic and Atmospheric Administration (Grant NA 16RG2255

Conic relaxations for transmission system planning

We apply lift-and-project type relaxations for polynomial optimization problems to AC transmission system planning, and obtain new second-order cone and semidefinite models. The models are compared to linear and nonlinear approaches on a six-bus test system.United States. Office of Naval Research (ONR Grant N00014-02-1-0623

Sampling-Based Coverage Path Planning for Inspection of Complex Structures

We present several new contributions in sampling-based coverage path planning, the task of finding feasible paths that give 100% sensor coverage of complex structures in obstacle-filled and visually occluded environments. First, we establish a framework for analyzing the probabilistic completeness of a sampling-based coverage algorithm, and derive results on the completeness and convergence of existing algorithms. Second, we introduce a new algorithm for the iterative improvement of a feasible coverage path; this relies on a sampling-based subroutine that makes asymptotically optimal local improvements to a feasible coverage path based on a strong generalization of the RRT algorithm. We then apply the algorithm to the real-world task of autonomous in-water ship hull inspection. We use our improvement algorithm in conjunction with redundant roadmap coverage planning algorithm to produce paths that cover complex 3D environments with unprecedented efficiency.United States. Office of Naval Research (ONR Grant N0014-06-10043

AC transmission system planning choosing lines from a discrete set

Transmission system planning (TSP) is a difficult nonlinear optimization problem involving non-convex quadratic terms, as well as discrete variables. We extend prior results for linear relaxations, drawing on a preliminary notional model of the power grid for the State of Florida. Realistic line choices necessitate a binary formulation, which is at the same time substantially more expensive than the mixed-integer counterpart and more accurate. In many cases, our relaxation directly generates a feasible solution; where it does not, we apply a practical load-deflation heuristic to recover strong solutions.United States. Office of Naval Research (Grant N00014-02-1-0623

A Single Differential Equation for First-Excursion Time in a Class of Linear Systems

First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times for a class of linear continuous, time-varying systems. In several examples, we show that the algorithm is both accurate and time-efficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.United States. Office of Naval Research (Grant N00014-02-1-0623

Multi-Goal Feasible Path Planning Using Ant Colony Optimization

A new algorithm for solving multi-goal planning problems in the presence of obstacles is introduced. We extend ant colony optimization (ACO) from its well-known application, the traveling salesman problem (TSP), to that of multi-goal feasible path planning for inspection and surveillance applications. Specifically, the ant colony framework is combined with a sampling-based point-to-point planning algorithm; this is compared with two successful sampling-based multi-goal planning algorithms in an obstacle-filled two-dimensional environment. Total mission time, a function of computational cost and the duration of the planned mission, is used as a basis for comparison. In our application of interest, autonomous underwater inspections, the ACO algorithm is found to be the best-equipped for planning in minimum mission time, offering an interior point in the tradeoff between computational complexity and optimality.United States. Office of Naval Research (Grant N00014-06-10043

Lift-and-Project Relaxations of AC Microgrid Distribution System Planning

We apply relaxation procedures to polynomial optimization problems that originate in transmission system planning, and obtain new convex formulations for the AC case. The approach is novel because the optimization is efficient but also addresses the true nonlinear physics directly. We illustrate the method on a test case derived from a notional shipboard distribution system

Linear relaxations for transmission system planning

We apply a linear relaxation procedure for polynomial optimization problems to transmission system planning. The approach recovers and improves upon existing linear models based on the DC approximation. We then consider the full AC problem, and obtain new linear models with nearly the same efficiency as the linear DC models. The new models are applied to standard test systems, and produce high-quality approximate solutions in reasonable computation time.United States. Office of Naval Research (Grant N00014-02-1-0623