arXiv subjects

Dariush Fooladivanda

Publications and source records attributed to Dariush Fooladivanda.

8 recordsLinked to original sources

arXiv2021

Data-driven Predictive Control for a Class of Uncertain Control-Affine Systems

This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are feasible and provide superior performance guarantees with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P). Further, we propose an efficient algorithm that provides online suboptimal data-driven solutions and guarantees performance with high probability. To illustrate the effectiveness of the proposed approach, we consider a highway speed-limit control problem. We then develop a set of data-driven speed controls that allow us to prevent traffic congestion with high probability. Finally, we employ the resulting control method on a traffic simulator to illustrate the effectiveness of this approach numerically.

math.OC↗

arXiv2021

Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems

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.

eess.SY↗

arXiv2020

Online Learning of Parameterized Uncertain Dynamical Environments with Finite-sample Guarantees

We present a novel online learning algorithm for a class of unknown and uncertain dynamical environments that are fully observable. First, we obtain a novel probabilistic characterization of systems whose mean behavior is known but which are subject to additive, unknown subGaussian disturbances. This characterization relies on recent concentration of measure results and is given in terms of ambiguity sets. Second, we extend the results to environments whose mean behavior is also unknown but described by a parameterized class of possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by learning the parametric dependence online, and retaining similar probabilistic guarantees with respect to the additive, unknown disturbance. We illustrate the results on a differential-drive robot subject to environmental uncertainty.

eess.SY↗

arXiv2019

Secure State Estimation and Control for Cyber Security of AC Microgrids

A timely, accurate, and secure dynamic state estimation is needed for reliable monitoring and efficient control of microgrids. The synchrophasor technology enables us to obtain synchronized measurements in real-time and to develop dynamic state estimators for real-time monitoring and control of microgrids. In this study, we consider an AC microgrid comprising several synchronous generators and inverter-interface power supplies, and focus on securely estimating the dynamic states of the microgrid from a set of corrupted data. We propose a dynamic state estimator which enables the microgrid operator to reconstruct the dynamic states of the microgrid from a set of corrupted data. Finally, we consider an AC microgrid with the same topology as the IEEE 33-bus distribution system, and numerically show that the proposed secure estimation algorithm can accurately reconstruct the attack signals.

eess.SY↗

arXiv2019

Joint User Association and Resource Allocation in Heterogeneous Cellular Networks: Comparison of Two Modeling Approaches

The performance of different combinations of user association (UA) and resource allocation (RA) in heterogeneous cellular networks has been extensively studied using a classic modeling approach based on system snapshots. There have been also many studies focusing on the dynamics of the system using queueing models. These modeling approaches are rarely compared with each other though they each bring different insights to the design problem. In this paper, we consider a queueing model-based approach to study the interplay of UA and RA, and compare the results to those obtained using snapshot models. Specifically, we formulate three different joint UA and RA optimization problems corresponding to the following three performance metrics: the maximum achievable arrival rate, the average system delay, and the maximum per-user delay. These problems are non-convex integer programs. We have therefore developed numerical techniques to compute either their exact solutions or tight lower bounds. We obtain results for different combinations of RA and UA schemes, and compare the trends with those obtained via the snapshot approach. The trends on RA are very similar, which we take as a cross-validation of the two modeling approaches for this kind of problem. The trends on user association are somewhat different which indicates a lack of robustness of the results and the need for a careful validation of UA models.

cs.NI↗

arXiv2018

Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.

math.OC↗

arXiv2018

Utilization of Water Supply Networks for Harvesting Renewable Energy

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.

eess.SY↗

arXiv2016

Secure State Estimation for Nonlinear Power Systems under Cyber Attacks

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.

eess.SY↗