Dariush Fooladivanda

Qie Hu, Dariush Fooladivanda, Young Hwan Chang et al.

This paper focuses on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements. In particular, we consider two broad classes of nonlinear systems, and propose a technique which enables us to perform secure state estimation for such nonlinear systems. We then provide guarantees on the achievable state estimation error against arbitrary corruptions, and analytically characterize the number of errors that can be perfectly corrected by a decoder. To illustrate how the proposed nonlinear estimation approach can be applied to practical systems, we focus on secure estimation for the wide area control of an interconnected power system under cyber-physical attacks and communication failures, and propose a secure estimator for the power system. Finally, we numerically show that the proposed secure estimation algorithm enables us to reconstruct the attack signals accurately.

Dariush Fooladivanda, Alejandro D. Domínguez-García, Peter W. Sauer

Renewable surplus power is increasing due to the increasing penetration of these intermittent resources. In practice, electric grid operators either curtail the surplus energy resulting from renewable-based generations or utilize energy storage resources to absorb it. In this paper, we propose a framework for utilizing water pumps and tanks in water supply networks to absorb the surplus electrical energy resulting from renewable-based electricity generation resources in the electrical grid. We model water supply networks analytically, and propose a two-step procedure that utilizes the water tanks in the water supply network to harvest the surplus energy from an electrical grid. In each step, the water network operator needs to solve an optimization problem that is non-convex. To compute optimal pump schedules and water flows, we develop a second-order cone relaxation and an approximation technique that enable us to transform the proposed problems into mixed-integer second-order cone programs. We then provide the conditions under which the proposed relaxation is exact, and present an algorithm for constructing an exact solution to the original problem from a solution to the relaxed problem. We demonstrate the effectiveness of the proposed framework via numerical simulations.

Dan Li, Dariush Fooladivanda, Sonia Martinez

This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set using a finite historical data set, and its use to make online decisions with probabilistic regret function bounds. Leveraging the merits of Machine Learning, the main technical approach relies on the theory of Distributional Robust Optimization (DRO), to hedge against uncertainty and provide less conservative results than standard Robust Optimization approaches. Starting from recent results that describe ambiguity sets via parameterized, and control-dependent empirical distributions as well as ambiguity radii, we first present a tractable reformulation of the corresponding optimization problem while maintaining the probabilistic guarantees. We then specialize these problems to the cases of 1) optimal one-stage control of distributionally uncertain nonlinear systems, and 2) resource allocation under distributional uncertainty. A novelty of this work is that it extends DRO to online optimization problems subject to a distributionally uncertain dynamical system constraint, handled via a control-dependent ambiguity set that leads to online-tractable optimization with probabilistic guarantees on regret bounds. Further, we introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.