A Scalable Semidefinite Relaxation Approach to Grid Scheduling

Determination of the most economic strategies for supply and transmission of electricity is a daunting computational challenge. Due to theoretical barriers, so-called NP-hardness, the amount of effort to optimize the schedule of generating units and route of power, can grow exponentially with the number of decision variables. Practical approaches to this problem involve legacy approximations and ad-hoc heuristics that may undermine the efficiency and reliability of power system operations, that are ever growing in scale and complexity. Therefore, the development of powerful optimization methods for detailed power system scheduling is critical to the realization of smart grids and has received significant attention recently. In this paper, we propose for the first time a computational method, which is capable of solving large-scale power system scheduling problems with thousands of generating units, while accurately incorporating the nonlinear equations that govern the flow of electricity on the grid. The utilization of this accurate nonlinear model, as opposed to its linear approximations, results in a more efficient and transparent market design, as well as improvements in the reliability of power system operations. We design a polynomial-time solvable third-order semidefinite programming (TSDP) relaxation, with the aim of finding a near globally optimal solution for the original NP-hard problem. The proposed method is demonstrated on the largest available benchmark instances from real-world European grid data, for which provably optimal or near-optimal solutions are obtained

Real-Time Stochastic Optimal Control for Multi-agent Quadrotor Systems

This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as velocity sequences, and a platform-specific low-level controller which ensures that these velocity sequences are met. The planning task is expressed as a centralized path-integral control problem, for which optimal control computation corresponds to a probabilistic inference problem that can be solved by efficient sampling methods. Through simulation we show that our SOC approach (a) has significant benefits compared to deterministic control and other SOC methods in multimodal problems with noise-dependent optimal solutions, (b) is capable of controlling a large number of platforms in real-time, and (c) yields collective emergent behaviour in the form of flight formations. Finally, we show that our approach works for real platforms, by controlling a team of three quadrotors in outdoor conditions.Comment: 17 pages, 8 figures, 26th International Conference on Automated Planning and Schedulin

On the Flow Problem in Water Distribution Networks: Uniqueness and Solvers

Increasing concerns on the security and quality of water distribution systems (WDS), along with their role as smart city components, call for computational tools with performance guarantees. To this end, this work revisits the physical laws governing water flow and provides a hierarchy of solvers having complementary value. Given water injections in a WDS, finding the corresponding water flows within pipes and pumps together with the pressures at all nodes constitutes the water flow (WF) problem. The latter entails solving a set of (non)-linear equations. It is shown that the WF problem admits a unique solution even in networks hosting pumps. For networks without pumps, the WF solution can be recovered as the minimizer of a convex energy function. The latter approach is extended to networks with pumps but not in cycles, through a stitching algorithm. For networks with non-overlapping cycles, a provably exact convex relaxation of the pressure drop equations yields a mixed-integer quadratic program (MIQP)-based WF solver. A hybrid scheme combining the MIQP with the stitching algorithm can handle water networks with overlapping cycles, but without pumps on them. Each solver is guaranteed to converge regardless initialization. Two of the solvers are numerically validated on a benchmark WDS

Context-Aware System Synthesis, Task Assignment, and Routing

The design and organization of complex robotic systems traditionally requires laborious trial-and-error processes to ensure both hardware and software components are correctly connected with the resources necessary for computation. This paper presents a novel generalization of the quadratic assignment and routing problem, introducing formalisms for selecting components and interconnections to synthesize a complete system capable of providing some user-defined functionality. By introducing mission context, functional requirements, and modularity directly into the assignment problem, we derive a solution where components are automatically selected and then organized into an optimal hardware and software interconnection structure, all while respecting restrictions on component viability and required functionality. The ability to generate \emph{complete} functional systems directly from individual components reduces manual design effort by allowing for a guided exploration of the design space. Additionally, our formulation increases resiliency by quantifying resource margins and enabling adaptation of system structure in response to changing environments, hardware or software failure. The proposed formulation is cast as an integer linear program which is provably $\mathcal{NP}$-hard. Two case studies are developed and analyzed to highlight the expressiveness and complexity of problems that can be addressed by this approach: the first explores the iterative development of a ground-based search-and-rescue robot in a variety of mission contexts, while the second explores the large-scale, complex design of a humanoid disaster robot for the DARPA Robotics Challenge. Numerical simulations quantify real world performance and demonstrate tractable time complexity for the scale of problems encountered in many modern robotic systems.Comment: 17 pages, 10 figures, Submitted to Transactions in Robotic

A Convex Optimization Approach to Smooth Trajectories for Motion Planning with Car-Like Robots

In the recent past, several sampling-based algorithms have been proposed to compute trajectories that are collision-free and dynamically-feasible. However, the outputs of such algorithms are notoriously jagged. In this paper, by focusing on robots with car-like dynamics, we present a fast and simple heuristic algorithm, named Convex Elastic Smoothing (CES) algorithm, for trajectory smoothing and speed optimization. The CES algorithm is inspired by earlier work on elastic band planning and iteratively performs shape and speed optimization. The key feature of the algorithm is that both optimization problems can be solved via convex programming, making CES particularly fast. A range of numerical experiments show that the CES algorithm returns high-quality solutions in a matter of a few hundreds of milliseconds and hence appears amenable to a real-time implementation

Efficient Model Identification for Tensegrity Locomotion

This paper aims to identify in a practical manner unknown physical parameters, such as mechanical models of actuated robot links, which are critical in dynamical robotic tasks. Key features include the use of an off-the-shelf physics engine and the Bayesian optimization framework. The task being considered is locomotion with a high-dimensional, compliant Tensegrity robot. A key insight, in this case, is the need to project the model identification challenge into an appropriate lower dimensional space for efficiency. Comparisons with alternatives indicate that the proposed method can identify the parameters more accurately within the given time budget, which also results in more precise locomotion control

Thermal Transients in District Heating Systems

Heat fluxes in a district heating pipeline systems need to be controlled on the scale from minutes to an hour to adjust to evolving demand. There are two principal ways to control the heat flux - keep temperature fixed but adjust velocity of the carrier (typically water) or keep the velocity flow steady but then adjust temperature at the heat producing source (heat plant). We study the latter scenario, commonly used for operations in Russia and Nordic countries, and analyze dynamics of the heat front as it propagates through the system. Steady velocity flows in the district heating pipelines are typically turbulent and incompressible. Changes in the heat, on either consumption or production sides, lead to slow transients which last from tens of minutes to hours. We classify relevant physical phenomena in a single pipe, e.g. turbulent spread of the turbulent front. We then explain how to describe dynamics of temperature and heat flux evolution over a network efficiently and illustrate the network solution on a simple example involving one producer and one consumer of heat connected by "hot" and "cold" pipes. We conclude the manuscript motivating future research directions.Comment: 31 pages, 7 figure

The role of intelligent systems in delivering the smart grid

The development of "smart" or "intelligent" energy networks has been proposed by both EPRI's IntelliGrid initiative and the European SmartGrids Technology Platform as a key step in meeting our future energy needs. A central challenge in delivering the energy networks of the future is the judicious selection and development of an appropriate set of technologies and techniques which will form "a toolbox of proven technical solutions". This paper considers functionality required to deliver key parts of the Smart Grid vision of future energy networks. The role of intelligent systems in providing these networks with the requisite decision-making functionality is discussed. In addition to that functionality, the paper considers the role of intelligent systems, in particular multi-agent systems, in providing flexible and extensible architectures for deploying intelligence within the Smart Grid. Beyond exploiting intelligent systems as architectural elements of the Smart Grid, with the purpose of meeting a set of engineering requirements, the role of intelligent systems as a tool for understanding what those requirements are in the first instance, is also briefly discussed

A SPEA2 Based Planning Framework for Optimal Integration of Distributed Generations

The paper presents a multi-objective optimisation method for analysing the best mix of renewable and non- renewable distributed generations (DG) in a distribution network. The method aims at minimising the total cost of the real power generation, line losses and CO2 emissions, and maximising the benefits from DG installations over a planning horizon of 20 years. The paper proposes new objective functions that take into account the longevity of DG operations as one of its selection criteria. The analysis utilises the Strength Pareto Evolutionary Algorithm 2 (SPEA2) for optimisation and MATPOWER for solving the optimal power flow problems

A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity

The key challenge in multiagent learning is learning a best response to the behaviour of other agents, which may be non-stationary: if the other agents adapt their strategy as well, the learning target moves. Disparate streams of research have approached non-stationarity from several angles, which make a variety of implicit assumptions that make it hard to keep an overview of the state of the art and to validate the innovation and significance of new works. This survey presents a coherent overview of work that addresses opponent-induced non-stationarity with tools from game theory, reinforcement learning and multi-armed bandits. Further, we reflect on the principle approaches how algorithms model and cope with this non-stationarity, arriving at a new framework and five categories (in increasing order of sophistication): ignore, forget, respond to target models, learn models, and theory of mind. A wide range of state-of-the-art algorithms is classified into a taxonomy, using these categories and key characteristics of the environment (e.g., observability) and adaptation behaviour of the opponents (e.g., smooth, abrupt). To clarify even further we present illustrative variations of one domain, contrasting the strengths and limitations of each category. Finally, we discuss in which environments the different approaches yield most merit, and point to promising avenues of future research.Comment: 64 pages, 7 figures. Under review since November 201