A Feedback-Based Regularized Primal-Dual Gradient Method for Time-Varying Nonconvex Optimization

This paper considers time-varying nonconvex optimization problems, utilized to model optimal operational trajectories of systems governed by possibly nonlinear physical or logical models. Algorithms for tracking a Karush-Kuhn-Tucker point are synthesized, based on a regularized primal-dual gradient method. In particular, the paper proposes a feedback-based primal-dual gradient algorithm, where analytical models for system state or constraints are replaced with actual measurements. When cost and constraint functions are twice continuously differentiable, conditions for the proposed algorithms to have bounded tracking error are derived, and a discussion of their practical implications is provided. Illustrative numerical simulations are presented for an application in power systems

A Feedback-Based Regularized Primal-Dual Gradient Method for Time-Varying Nonconvex Optimization

This paper considers time-varying nonconvex optimization problems, utilized to model optimal operational trajectories of systems governed by possibly nonlinear physical or logical models. Algorithms for tracking a Karush-Kuhn-Tucker point are synthesized, based on a regularized primal-dual gradient method. In particular, the paper proposes a feedback-based primal-dual gradient algorithm, where analytical models for system state or constraints are replaced with actual measurements. When cost and constraint functions are twice continuously differentiable, conditions for the proposed algorithms to have bounded tracking error are derived, and a discussion of their practical implications is provided. Illustrative numerical simulations are presented for an application in power systems

Group sparse Lasso for cognitive network sensing robust to model uncertainties and outliers

PostprintTo account for variations in the frequency, time, and space dimensions, dynamic re-use of licensed bands under the cognitive radio (CR) paradigm calls for innovative network-level sensing algorithms for multi-dimensional spectrum opportunity awareness. Toward this direction, the present paper develops a collaborative scheme whereby CRs cooperate to localize active primary user (PU) transmitters and reconstruct a power spectral density (PSD) map portraying the spatial distribution of power across the monitored area per frequency band and channel coherence interval. The sensing scheme is based on a parsimonious model that accounts for two forms of sparsity: one due to the narrow-band nature of transmit-PSDs compared to the large portion of spectrum that a CR can sense, and another one emerging when adopting a spatial grid of candidate PU locations. Capitalizing on this dual sparsity, an estimator of the model coefficients is obtained based on the group sparse least-absolute-shrinkage-and-selection operator (GS-Lasso). A novel reduced-complexity GS-Lasso solver is developed by resorting to the alternating direction method of multipliers (ADMoM). Robust versions of this GS-Lasso estimator are also introduced using a GS total least-squares (TLS) approach to cope with both uncertainty in the regression matrices, arising due to inaccurate channel estimation and grid-mismatch effects, and unexpected model outliers. In spite of the non-convexity of the GS-TLS criterion, the novel robust algorithm has guaranteed convergence to (at least) a local optimum. The analytical findings are corroborated by numerical test

Renewable-based charging in green ride-sharing

Abstract Governments, regulatory bodies, and manufacturers are proposing plans to accelerate the adoption of electric vehicles (EVs), with the goal of reducing the impact of greenhouse gases and pollutants from internal combustion engines on human health and climate change. In this context, the paper considers a scenario where ride-sharing enterprises utilize a 100%-electrified fleet of vehicles, and seeks responses to the following key question: How can renewable-based EV charging be maximized without disrupting the quality of the ride-sharing services? We propose a new mechanism to promote EV charging during hours of high renewable generation, and we introduce the concept of charge request, which is issued by a power utility company. Our mechanism is inspired by a game-theoretic approach where the power utility company proposes incentives and the ride-sharing platform assigns vehicles to both ride and charge requests; the bargaining mechanism leads to prices and EV assignments that are aligned with the notion of Nash equilibria. Numerical results show that it is possible to shift the EV charging during periods of high renewable generation and adapt to intermittent generation while minimizing the impact on the quality of service. The paper also investigates how the users’ willingness to ride-share affects the charging strategy and the quality of service

Novel use of online optimization in a mathematical model of COVID-19 to guide the relaxation of pandemic mitigation measures

Since early 2020, non-pharmaceutical interventions (NPIs)—implemented at varying levels of severity and based on widely-divergent perspectives of risk tolerance—have been the primary means to control SARS-CoV-2 transmission. This paper aims to identify how risk tolerance and vaccination rates impact the rate at which a population can return to pre-pandemic contact behavior. To this end, we developed a novel mathematical model and we used techniques from feedback control to inform data-driven decision-making. We use this model to identify optimal levels of NPIs across geographical regions in order to guarantee that hospitalizations will not exceed given risk tolerance thresholds. Results are shown for the state of Colorado, United States, and they suggest that: coordination in decision-making across regions is essential to maintain the daily number of hospitalizations below the desired limits; increasing risk tolerance can decrease the number of days required to discontinue NPIs, at the cost of an increased number of deaths; and if vaccination uptake is less than 70%, at most levels of risk tolerance, return to pre-pandemic contact behaviors before the early months of 2022 may newly jeopardize the healthcare system. The sooner we can acquire population-level vaccination of greater than 70%, the sooner we can safely return to pre-pandemic behaviors