### Automated Water Management

Conservation of water resources is critical in many places of the world, including the American West. Current technologies enabling flow instrumentation and the remote control of automated gates and release mechanisms at dams facilitate our systematic modeling and control of complex river systems. Real-time flow data related to our work for the modeling and control of the Piute Reservoir and the Sevier River in Central Utah can be found at www.sevierriver.org.

### Coalition Robustness of Multiagent Systems

This research explores the interplay of cooperation and competition in multiagent dynamics. Our study begins with the stability robustness of multiagent systems with respect to uncertain coalition structure. Such systems arise naturally from a variety of compartmental models, including those used in security analysis, economics, ecology, etc. Moreover, coalition robustness becomes significant when conducting organizational analysis, such as in merger simulation, market structure analysis, or in other areas of industrial organization.

#### Papers

- Stability Robustness Conditions for Gradient Play Differential Games with Partial Participation in Coalitions
- Coalition Robustness of Multiagent Systems
- Stability Robustness Conditions for Market Power Analysis in Industrial Organization Networks
- Cooperation-based Clustering for Profit-Maximizing Organizational Design

### Cyber Security of Distributed Network Systems

Engineered systems are increasingly complex, with distributed sensing, computation, and actuation nodes linked by communication networks. This project considers how the structure and dynamics of the system relate to its vulnerability to attack, where an attacker’s objectives may include destabilization, state hijacking, or system inference attacks.

### Demand Forecasting

Predictive modeling is essential for rational decision making, since understanding the consequences of various options is the first step toward choosing between them. Merchants need such models to understand how pricing and other decisions will impact revenue generated in their respective markets. This project details known algorithms for using a finite record of sales data to generate predictive models and forecast demand.

### Dynamic Pricing

Changing prices of a good or service allows a firm to gather information about the market demand for the product, but knowledge of market demand motivates fixing the price at its profit-maximizing value. This project explores tradeoffs in exploration versus exploitation of market information and helps a firm understand how the dynamic, feedback structure of economic interaction influences effective pricing decisions. This work has included collaboration with the Applied Machine Learning Laboratory at BYU.

### Ellipsometry-Driven Feedback Control of Epitaxial Processes

Epitaxy is a process for depositing atomic-scale films of a specified composition on a wafer substrate. Meticulously growing a particular ‘sandwich’ of nanofilms is a critical step in the production of many semiconductor devices. Nevertheless, one often does not know if the deposited film has the right properties, such as thickness and material composition, until growth is completed. This work uses in-situ ellipsometry, an optical device for probing film-growth as it occurs, to adjust epitaxy process parameters in real-time to guarantee that the actual film grows as planned.

### Factory Optimization

Flexible production systems use the same sequence of machines to produce different products. The recipe for making each product, however, may tie up each machine differently, skip some machines, or require reprocessing on certain machines. Moreover, the factory may contain multiple copies of a given machine that operate in parallel (to speed up that stage of production), different machines may process different batch sizes of different products, and there may or may not be temporary storage facilities between machines. Scheduling the optimal production sequence to manufacture a specified quota for each type of product is computationally difficult; we explore efficient approximations for this and related problems. This includes how to best invest resources for additional machines, or how to determine how operational constraints on the duration of the workday and workweek affect the optimal schedule and the associated return on investment of the capital equipment in the factory.

#### Papers

- Model Approximation for Batch Flow Shop Scheduling with Fixed Batch Sizes
- A Dynamic Workflow Framework for Mass Customization Using Web Service and Autonomous Agent
- An Approximation Method for Sequencing of a Batch Manufacturing System
- Model Reduction for a Class of Input-Quantized Systems in the Max-Plus Algebra
- Monotonically Improving Error Bounds for a Sequence of Approximations for Makespan Minimization of Batch Manufacturing Systems
- A Decision-Friendly Approximation Technique for Scheduling Multipurpose Batch Manufacturing Systems

### Federal Reserve Policy

Good monetary policy is crucial to low inflation, high employment, and stable economic growth. The Federal Reserve puts its policy into effect on a daily basis through the use of Open Market Operations, which indirectly controls our nation’s money supply through the buying and selling of securities in our nation’s banking system. The purpose of this project is to model this process as a dynamical system and then explore how to control our monetary policies algorithmically.

### Forecasting Political Instability

Creating and analyzing models of international political conflict is a valuable problem because understanding the dynamics of such systems can be an invaluable aid to appropriately interpret political behavior. The challenge is to create a tractable method that retains political meaning and preserves enough information of the underlying dynamic system so as to support the development of predictive models. This project is building a control-theoretic model for the Israeli-Palestinian conflict that is amenable to optimization and expresses the tradeoff between internal and external coalition strength.

### Geometric Limits of Performance for Path Control

Tracking problems use feedback control to drive a system to follow a specified time trajectory. Sometimes, however, one is only interested in how well the system stayed on the specified path, and not necessarily when it transversed each point along the path. If we allow a tracking system to speed up or slow down, as necessary, to transverse a given curve within a fixed completion time, we find a trade off between the geometric shape of the curve and the path error incurred by the system. This work investigates this tradeoff and defines fundamental limits of performance.

### Inventory Management

The purpose of this project is to connect inventory management problems to those of mathematical finance. For example, there are close similarities between the classical Newsvendor Problem in operations research and that of pricing a European put option in math finance. The goal of this project is to rigorously connect inventory management problems in operations research to portfolio management problems in math finance, and explore the use of traditional and exotic investment vehicles as way to manage inventories and hedge the risks associated with selling and distributing real goods in the market.

### Laser Stabilization

Diode lasers typically suffer from wavelength drift and exhibit a line width that is too broad to drive the atomic transitions in an atom interferometer. This project, in collaboration with Professor Dallin Durfee of BYU’s Physics Department, uses feedback control to stabilize the wavelength and narrow the line width of a side-emitting Grating-Stabilized External-Cavity Diode Laser.

### Market Making as a Dynamical System

In the capital markets, financial intermediaries such as market specialists, banks, and other financial services companies provide both a bid price and an ask price on the securities that they broker. The difference between these two prices is called the bid-ask spread; it essentially represents fees that are passed on to the buyers and sellers to account for the intermediaries’ market risk, transaction costs and inventory costs. The purpose of this project is to model the market making problem as a dynamical system and then to explore how to automate the clearing of markets as an Algorithmic Decision Process.

### Markov Approximation

Hidden Markov Models are a powerful tool for describing the behavior of many autonomous systems, including speech, internet traffic, and microbiological mechanisms such as protein structure or DNA sequence patterns. While asymptotically consistent algorithms exist for estimating the parameters of an HMM from data, such algorithms demand that the true system generating the data is in the class of models being explored. Typically, however, mathematical models are necessarily simplifications of the true system. This work investigates the nature of low order Hidden Markov Models that approximate the behavior of higher-order HMMs, and the impact of such approximations on the performance of the associated learning algorithms.

### Modeling, Identification, and Control of Crop Systems

Crop systems are a special class of production systems that depend on plant genetics, local ecology, soil chemistry, physical topography, weather, and management practices. Understanding these systems is particularly important to support an exploding global population without destroying natural resources. Moreover, new technologies bring new opportunities for sensing, actuating, and driving decisions with extensive data reserves. This project considers the modeling, identification and control of these complex systems.

### Network Reconstruction

One of the key problems in analyzing complex systems is estimating a system’s network structure given only input/output data. This problem arises in a variety of applications, but especially in systems biology where scientists want to understand how various protein interactions and signaling “pathways” result in particular cellular dynamics. This project, in collaboration with Professor Jorge Goncalves and the Control Systems Group at Cambridge University, explores implications of the graphical structure of a decision processes on the achievable dynamics of the entire system.

#### Papers

- Robust Signal-Structure Reconstruction
- On the Necessity of Full-State Measurement for State-Space Network Reconstruction
- Dynamical Structure Function Identifiability Conditions Enabling Signal Structure Reconstruction
- Necessary and Sufficient Informativity Conditions for Robust Network Reconstruction Using Dynamical Structure Functions
- Analysis and Design Tools for Structured Feedback Systems
- Robust Dynamical Network Structure Reconstruction
- Validation of Dynamical Structure Functions for the Reconstruction of Biochemical Networks
- Mathematical Relationships Between Representations of Structure in Linear Interconnected Dynamical Systems
- Representing Structure in Linear Interconnected Dynamical Systems
- A Comparison of Network Reconstruction Methods for Chemical Reaction Networks
- Network Structure Preserving Model Reduction with Weak A Priori Structural Information
- Network Structure Preserving Model Reduction: Results of a Simulation Study
- Minimal Realisation of Dynamical Structure Functions and Its Application to Network Reconstruction from Data
- Necessary and Sufficient Conditions for Dynamical Structure Reconstruction of LTI Networks
- Dynamical Structure Analysis of Sparsity and Minimality Heuristics for Reconstruction of Biochemical Networks
- Application and Properties of Dynamical Structure Functions
- Dynamical Structure Functions for the Reverse Engineering of LTI Networks

### Press-Sheet Optimization for Industrial-Scale Printing

Industrial-scale gang-run printing demands that orders for different products be combined in efficient ways to minimize waste and the associated production costs. Bad choices about which products to print now can lead to the need for wasteful runs in the future. This project approaches this issue as an open-loop control problem, with solutions drawn from integer linear programming.

### Retail Instrumentation: Design of a Loyalty Program

Although virtually every merchant collects and warehouses sales data, often such data is not informative enough to guide merchandising and marketing decisions. The missing link is knowing who is buying what. Loyalty programs offer incentives to customers in exchange for exactly this kind of information. This project explores the design of such incentives to minimize the corporate cost of fully instrumenting their operations.

### Retail Laboratory

Laboratories are widely available for biology, chemistry, and physics. This project develops the blueprints for, and implements, the first-of-its-kind economic laboratory for retail. We begin by making the subtle but important distinction between a laboratory, that uses controlled experimentation to generate new data about a phenomenon, and data processing algorithms that mine warehoused data for understanding. Every merchandising and marketing decision is based explicitly or implicitly on a model, or expectations, of how the market will react; the purpose of a laboratory is to verify that this model is good enough to make the proposed decisions worthwhile. We draw on the feedback structure of retail, between a firm and its market, to develop a concrete invalidation protocol, or marketing process, that allows decision makers to implement their ideas in a way that ensures errors in judgment become clear before they damage the enterprise. A prototype of these ideas is then executed at the on-campus retailer, the BYU Bookstore, to demonstrate their utility on a live retail operation; our retail laboratory is a real, functioning venture. Partners on the project include the Data Mining Laboratory at BYU.

### Software Verification

Verification that software works as designed to control external devices is critical in a variety of settings. Yet the complexity and shear size of software applications today make such verification very difficult. It is especially important to ensure that errors in interactive software designed to control something, such as an airplane or a power plant or the brakes on a car, does not induce catastrophic failure. This project explores how the feedback structure of such software systems affects our approach to the verification problem. This work has been conducted in collaboration with BYU’s Verification & Validation Laboratory.

### Symbiosis

Symbiosis refers to the long term, close association of two or more individuals of different species. We are interested in learning about the network structure of cooperation in competitive environments from symbiotic interactions. Specifically, we have studied how leafcutter ants and the mutualistic fungus they cultivate are affected by populations of mutualistic bacteria and parasitic fungi. One of the species of parasitic fungi attack the bacteria, causing it to produce an antibiotic in self-defense that also happens to kill the other parasitic fungi. Understanding how to model these complex relationships suggests new ways for thinking about the “structure” of complex systems.

### Tour de Finance

This research explores the development of a virtual fund management system to benchmark investment controllers as algorithmic decision processes on live market data. While similar paper-trading competitions exist, the Tour de Finance system is unique in its use of a particular class of dynamical systems as a dynamic rating mechanism to help ensure that the system is fair and rewards real intelligence over dumb luck. On our website, a link is provided for those wishing to participate in the Tour by designing controllers to interact with the system as autonomous agents, each managing its own virtual fund.

### Video Streaming

Sending video over the internet typically requires protocols that chop the video content into segments and adjust the quality level for each segment. Higher quality segments demand more bandwidth, so variations in available bandwidth can result in poor playback performance. This project considers control policies for client quality selection schemes that determine whether a client should request more packets for a given segment, increasing the quality of that segment, or request packets for future segments, planning ahead for smooth playback.

### Wireless Mesh Networks

Wireless mesh networks provide a cost-efficient alternative to wired network infrastructures in several applications. However, because wireless signals broadcast can interfere with each other, current medium access control protocols result in serious deficiencies of fairness and under-utilization of the network. Much recent work in the literature has explored designing rate controllers for wireless networks based on mathematical optimization.

This project explores ways to improve the modeling of resource constraints on wireless networks in order to achieve more accurate optimization problems from which to base the rate controllers. It also seeks methods by which proposed controllers can be compared in a precise manner, and determining upper bounds on the performance of any controller.