Information Structure Design in Team Decision Problems

We consider a problem of information structure design in team decision problems and team games. We propose simple, scalable greedy algorithms for adding a set of extra information links to optimize team performance and resilience to non-cooperative and adversarial agents. We show via a simple counterexample that the set function mapping additional information links to team performance is in general not supermodular. Although this implies that the greedy algorithm is not accompanied by worst-case performance guarantees, we illustrate through numerical experiments that it can produce effective and often optimal or near optimal information structure modifications

Edge Selection in Bilinear Dynamical Networks

In large-scale networks, agents (e.g., sensors and actuators) and links (e.g., couplings and communication links) can fail or be (cyber-)attacked. In this paper, we focus on continuous-time bilinear networks, where additive disturbances model attack/uncertainty on agents/states (a.k.a. node disturbances) and multiplicative disturbances model attack/uncertainty on couplings between agents/states (a.k.a. link disturbances). We then investigate a network robustness notion in terms of the underlying digraph of the network, and structure of exogenous uncertainties/attacks. Specifically, we define the robustness measure using the H2-norm of the network and calculate it in terms of the reachability Gramian of the bilinear system. The main result shows that under certain conditions, the measure is supermodular over the set of all possible attacked links. The supermodular property facilitates the efficient solution finding of the optimization problem. We conclude the paper with a few examples illustrating how different structures can make the system more or less vulnerable to malicious attacks on links and present our concluding remarks.Comment: 6 pages, 2 figure

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary documents) that explains an error in a proof of the original paper and provides a counterexample to the corresponding resul

Topology Design for Optimal Network Coherence

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of the network topology. As a consequence, a simple greedy algorithm is guaranteed to produce near optimal edge set selections. We also show that fast rank one updates of the Laplacian pseudoinverse using generalizations of the Sherman-Morrison formula and an accelerated variant of the greedy algorithm can speed up the algorithm by several orders of magnitude in practice. These allow our algorithms to scale to network sizes far beyond those that can be handled by convex relaxation heuristics

Optimizing resource allocation in computational sustainability: Models, algorithms and tools

The 17 Sustainable Development Goals laid out by the United Nations include numerous targets as well as indicators of progress towards sustainable development. Decision-makers tasked with meeting these targets must frequently propose upfront plans or policies made up of many discrete actions, such as choosing a subset of locations where management actions must be taken to maximize the utility of the actions. These types of resource allocation problems involve combinatorial choices and tradeoffs between multiple outcomes of interest, all in the context of complex, dynamic systems and environments. The computational requirements for solving these problems bring together elements of discrete optimization, large-scale spatiotemporal modeling and prediction, and stochastic models. This dissertation leverages network models as a flexible family of computational tools for building prediction and optimization models in three sustainability-related domain areas: 1) minimizing stochastic network cascades in the context of invasive species management; 2) maximizing deterministic demand-weighted pairwise reachability in the context of flood resilient road infrastructure planning; and 3) maximizing vertex-weighted and edge-weighted connectivity in wildlife reserve design. We use spatially explicit network models to capture the underlying system dynamics of interest in each setting, and contribute discrete optimization problem formulations for maximizing sustainability objectives with finite resources. While there is a long history of research on optimizing flows, cascades and connectivity in networks, these decision problems in the emerging field of computational sustainability involve novel objectives, new combinatorial structure, or new types of intervention actions. In particular, we formulate a new type of discrete intervention in stochastic network cascades modeled with multivariate Hawkes processes. In conjunction, we derive an exact optimization approach for the proposed intervention based on closed-form expressions of the objective functions, which is applicable in a broad swath of domains beyond invasive species, such as social networks and disease contagion. We also formulate a new variant of Steiner Forest network design, called the budget-constrained prize-collecting Steiner forest, and prove that this optimization problem possesses a specific combinatorial structure, restricted supermodularity, that allows us to design highly effective algorithms. In each of the domains, the optimization problem is defined over aspects that need to be predicted, hence we also demonstrate improved machine learning approaches for each.Ph.D

Determination of Design of Optimal Actuator Location Based on Control Energy

The thesis deals with the selection of the sets of inputs and outputs using the energy properties of the controllability and observability of a system and aims to define input and output structures which require minimization of the energy for control and state reconstruction. Such a study explores the energy dimension of the properties of controllability and observability, develops computations for the controllability and observability Gramians for stable and unstable systems and examines measures of the degree of controllability and observability properties using SVD (Singular Value Decomposition) of Gramians to compute the maximal and minimal energy requirements. These characterize the relative degree of controllability and observability under conditions where the available energy is constrained. The notion of energy surfaces in the state space is introduced and this enables the characterization of restricted notions of controllability and observability when the available energy is bounded. The maximal and minimal energy requirements for different input vectors is demonstrated and this provides the basis for the development of strategies and methodologies for selection of systems of inputs and outputs to minimize the energy required for control, respectively state reconstruction. These results enable the development of input, output structure selection methodology using a novel optimization method. This thesis contributes in the further development of the area of systems, or global instrumentation, developed so far based on the assignment of structural characteristics by incorporating the role of energy requirements. The research provides energy based tools for the selection of input and outputs schemes with a main criterion the minimization of the energy required for control and observation and thus provide an alternative approach based on quantitative system properties in characterizing control and state observation as functions of given sets of inputs and output sets. The methodologies developed may be used as design tools where apart from energy requirements other design criteria may be also incorporated for the selection of inputs and outputs. The methodology that is used is based on linear systems theory and tools from numerical linear algebra. The solution to the problems considered here is an integral part of the effort to develop an integrated approach to control and global process instrumentation