Chinwendu Enyioha

Chinwendu Enyioha, Mohammad Amin Rahimian, George J. Pappas et al.

In this paper, we study controllability of a network of linear single-integrator agents when the network size goes to infinity. We first investigate the effect of increasing size by injecting an input at every node and requiring that network controllability Gramian remain well-conditioned with the increasing dimension. We provide theoretical justification to the intuition that high degree nodes pose a challenge to network controllability. In particular, the controllability Gramian for the networks with bounded maximum degrees is shown to remain well-conditioned even as the network size goes to infinity. In the canonical cases of star, chain and ring networks, we also provide closed-form expressions which bound the condition number of the controllability Gramian in terms of the network size. We next consider the effect of the choice and number of leader nodes by actuating only a subset of nodes and considering the least eigenvalue of the Gramian as the network size increases. Accordingly, while a directed star topology can never be made controllable for all sizes by injecting an input just at a fraction $f<1$ of nodes; for path or cycle networks, the designer can actuate a non-zero fraction of nodes and spread them throughout the network in such way that the least eigenvalue of the Gramians remain bounded away from zero with the increasing size. The results offer interesting insights on the challenges of control in large networks and with high-degree nodes.

Chinwendu Enyioha, Ali Jadbabaie, Victor Preciado et al.

We present a distributed resource allocation strategy to control an epidemic outbreak in a networked population based on a Distributed Alternating Direction Method of Multipliers (D-ADMM) algorithm. We consider a linearized Susceptible- Infected-Susceptible (SIS) epidemic spreading model in which agents in the network are able to allocate vaccination resources (for prevention) and antidotes (for treatment) in the presence of a contagion. We express our epidemic control condition as a spectral constraint involving the Perron-Frobenius eigenvalue, and formulate the resource allocation problem as a Geometric Program (GP). Next, we separate the network-wide optimization problem into subproblems optimally solved by each agent in a fully distributed way. We conclude the paper by illustrating performance of our solution framework with numerical simulations.

Sindri Magnusson, Chinwendu Enyioha, Kathryn Heal et al.

Typical coordination schemes for future power grids require two-way communications. Since the number of end power-consuming devices is large, the bandwidth requirements for such two-way communication schemes may be prohibitive. Motivated by this observation, we study distributed coordination schemes that require only one-way limited communications. In particular, we investigate how dual descent distributed optimization algorithm can be employed in power networks using one-way communication. In this iterative algorithm, system coordinators broadcast coordinating (or pricing) signals to the users/devices who update power consumption based on the received signal. Then system coordinators update the coordinating signals based on the physical measurement of the aggregate power usage. We provide conditions to guarantee the feasibility of the aggregated power usage at each iteration so as to avoid blackout. Furthermore, we prove the convergence of algorithms under these conditions, and establish its rate of convergence. We illustrate the performance of our algorithms using numerical simulations. These results show that one-way limited communication may be viable for coordinating/operating the future smart grids.

Chinwendu Enyioha, Sindri Magnusson, Kathryn Heal et al.

As independent service providers shift from conventional energy to renewable energy sources, the power distribution system will likely experience increasingly significant fluctuation in supply, given the uncertain and intermittent nature of renewable sources like wind and solar energy. These fluctuations in power generation, coupled with time-varying consumer demands of electricity and the massive scale of power distribution networks present the need to not only design real-time decentralized power allocation algorithms, but also characterize how effective they are given fast-changing consumer demands and power generation capacities. In this paper, we present an Online Decentralized Dual Descent (OD3) power allocation algorithm and determine (in the worst case) how much of observed social welfare and price volatility can be explained by fluctuations in generation capacity and consumer demand. Convergence properties and performance guarantees of the OD3 algorithm are analyzed by characterizing the difference between the online decision and the optimal decision. The theoretical results in the paper are validated and illustrated by numerical experiments using real data.

Victor M. Preciado, Michael Zargham, Chinwendu Enyioha et al.

In this chapter, we consider the problem of designing protection strategies to contain spreading processes in complex cyber-physical networks. We illustrate our ideas using a family of bio-motivated spreading models originally proposed in the epidemiological literature, e.g., the Susceptible-Infected-Susceptible (SIS) model. We first introduce a framework in which we are allowed to distribute two types of resources in order to contain the spread, namely, (i) preventive resources able to reduce the spreading rate, and (ii) corrective resources able to increase the recovery rate of nodes in which the resources are allocated. In practice, these resources have an associated cost that depends on either the resiliency level achieved by the preventive resource, or the restoration efficiency of the corrective resource. We present a mathematical framework, based on dynamic systems theory and convex optimization, to find the cost-optimal distribution of protection resources in a network to contain the spread. We also present two extensions to this framework in which (i) we consider generalized epidemic models, beyond the simple SIS model, and (ii) we assume uncertainties in the contact network in which the spreading is taking place. We compare these protection strategies with common heuristics previously proposed in the literature and illustrate our results with numerical simulations using the air traffic network.

Suraj Singireddy, Precious Nwaorgu, Andre Beckus et al.

Reinforcement learning (RL) is a powerful tool for finding optimal policies in sequential decision processes. However, deep RL methods have two weaknesses: collecting the amount of agent experience required for practical RL problems is prohibitively expensive, and the learned policies exhibit poor generalization on tasks outside the training data distribution. To mitigate these issues, we introduce automaton distillation, a form of neuro-symbolic transfer learning in which Q-value estimates from a teacher are distilled into a low-dimensional representation in the form of an automaton. We then propose methods for generating Q-value estimates where symbolic information is extracted from a teacher's Deep Q-Network (DQN). The resulting Q-value estimates are used to bootstrap learning in the target discrete and continuous environment via a modified DQN and Twin-Delayed Deep Deterministic (TD3) loss function, respectively. We demonstrate that automaton distillation decreases the time required to find optimal policies for various decision tasks in new environments, even in a target environment different in structure from the source environment.

Devin Hunter, Chinwendu Enyioha

Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation. With the ever-increasing incorporation of these data-driven models into the estimation domain, model predictions with reliable margins of error are a requirement -- especially for safety-critical applications. This paper discusses the application of a novel real-time, data-driven estimation approach based on the multi-fidelity residual physics-informed neural process (MFR-PINP) toward the real-time state estimation of a robotic system. Specifically, we address the model-mismatch issue of selecting an accurate kinematic model by tasking the MFR-PINP to also learn the residuals between simple, low-fidelity predictions and complex, high-fidelity ground-truth dynamics. To account for model uncertainty present in a physical implementation, robust uncertainty guarantees from the split conformal (SC) prediction framework are modeled in the training and inference paradigms. We provide implementation details of our MFR-PINP-based estimator for a hybrid online learning setting to validate our model's usage in real-time applications. Experimental results of our approach's performance in comparison to the state-of-the-art variants of the Kalman filter (i.e. unscented Kalman filter and deep Kalman filter) in estimation scenarios showed promising results for the MFR-PINP model as a viable option in real-time estimation tasks.