Control and optimization approaches for energy-limited systems: applications to wireless sensor networks and battery-powered vehicles

This dissertation studies control and optimization approaches to obtain energy-efficient and reliable routing schemes for battery-powered systems in network settings. First, incorporating a non-ideal battery model, the lifetime maximization problem for static wireless sensor networks is investigated. Adopting an optimal control approach, it is shown that there exists a time-invariant optimal routing vector in a fixed topology network. Furthermore, under very mild conditions, this optimal policy is robust with respect to the battery model used. Then, the lifetime maximization problem is investigated for networks with a mobile source node. Redefining the network lifetime, two versions of the problem are studied: when there exist no prior knowledge about the source node’s motion dynamics vs. when source node’s trajectory is known in advance. For both cases, problems are formulated in the optimal control framework. For the former, the solution can be reduced to a sequence of nonlinear programming problems solved on line as the source node trajectory evolves. For the latter, an explicit off-line numerical solution is required. Second, the problem of routing for vehicles with limited energy through a network with inhomogeneous charging nodes is studied. The goal is to minimize the total elapsed time, including traveling and recharging time, for vehicles to reach their destinations. Adopting a game-theoretic approach, the problem is investigated from two different points of view: user-centric vs. system-centric. The former is first formulated as a mixed integer nonlinear programming problem. Then, by exploiting properties of an optimal solution, it is reduced to a lower dimensionality problem. For the latter, grouping vehicles into subflows and including the traffic congestion effects, a system-wide optimization problem is defined. Both problems are studied in a dynamic programming framework as well. Finally, the thesis quantifies the Price Of Anarchy (POA) in transportation net- works using actual traffic data. The goal is to compare the network performance under user-optimal vs. system-optimal policies. First, user equilibria flows and origin- destination demands are estimated for the Eastern Massachusetts transportation net- work using speed and capacity datasets. Then, obtaining socially-optimal flows by solving a system-centric problem, the POA is estimated

Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into "subflows". We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control and Automation, MED'1

Lifetime Maximization of Wireless Sensor Networks with a Mobile Source Node

We study the problem of routing in sensor networks where the goal is to maximize the network's lifetime. Previous work has considered this problem for fixed-topology networks. Here, we add mobility to the source node, which requires a new definition of the network lifetime. In particular, we redefine lifetime to be the time until the source node depletes its energy. When the mobile node's trajectory is unknown in advance, we formulate three versions of an optimal control problem aiming at this lifetime maximization. We show that in all cases, the solution can be reduced to a sequence of Non- Linear Programming (NLP) problems solved on line as the source node trajectory evolves.Comment: A shorter version of this work will be published in Proceedings of 2016 IEEE Conference on Decision and Contro

Data-driven Estimation of Origin-Destination Demand and User Cost Functions for the Optimization of Transportation Networks

In earlier work (Zhang et al., 2016) we used actual traffic data from the Eastern Massachusetts transportation network in the form of spatial average speeds and road segment flow capacities in order to estimate Origin-Destination (OD) flow demand matrices for the network. Based on a Traffic Assignment Problem (TAP) formulation (termed "forward problem"), in this paper we use a scheme similar to our earlier work to estimate initial OD demand matrices and then propose a new inverse problem formulation in order to estimate user cost functions. This new formulation allows us to efficiently overcome numerical difficulties that limited our prior work to relatively small subnetworks and, assuming the travel latency cost functions are available, to adjust the values of the OD demands accordingly so that the flow observations are as close as possible to the solutions of the forward problem. We also derive sensitivity analysis results for the total user latency cost with respect to important parameters such as road capacities and minimum travel times. Finally, using the same actual traffic data from the Eastern Massachusetts transportation network, we quantify the Price of Anarchy (POA) for a much larger network than that in Zhang et al. (2016).Comment: Preprint submitted to The 20th World Congress of the International Federation of Automatic Control, July 9-14, 2017, Toulouse, Franc

The price of anarchy in transportation networks by estimating user cost functions from actual traffic data

We have considered a large-scale road network in Eastern Massachusetts. Using real traffic data in the form of spatial average speeds and the flow capacity for each road segment of the network, we converted the speed data to flow data and estimated the origin-destination flow demand matrices for the network. Assuming that the observed traffic data correspond to user (Wardrop) equilibria for different times-of-the-day and days-of-the-week, we formulated appropriate inverse problems to recover the per-road cost (congestion) functions determining user route selection for each month and time-of-day period. In addition, we analyzed the sensitivity of the total user latency cost to important parameters such as road capacities and minimum travel times. Finally, we formulated a system-optimum problem in order to find socially optimal flows for the network. We investigated the network performance, in terms of the total latency, under a user-optimal policy versus a system-optimal policy. The ratio of these two quantities is defined as the Price of Anarchy (POA) and quantifies the efficiency loss of selfish actions compared to socially optimal ones. Our findings contribute to efforts for a smarter and more efficient city

Optimal routing of electric vehicles in networks with charging nodes: A dynamic programming approach

Motivated by the significant role of recharging in battery-powered vehicles, we study the routing problem for vehicles with limited energy through a network of charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey.We have studied the case of homogeneous charging nodes in [1] and generalized it to inhomogeneous charging nodes in [2] by formulating and solving a Mixed Integer Non-Linear Programming problem (MINLP) for a single-vehicle. In this paper, we solve the same problem using Dynamic Programming (DP), resulting in optimal solutions with lower computational complexity compared to [2]. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into “subflows” and propose a DP formulation. Our numerical results show that DP becomes prohibitively slow as the number of subflows increases. As in [1] and [2] we resort to an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss of accuracy