pwc-archive/papers-with-abstracts huggingface dataset:
Distributed Optimization for Quadratic Cost Functions over Large-Scale Networks with Quantized Communication and Finite-Time Convergence
Authors: Apostolos I. Rikos, Andreas Grammenos, Evangelia Kalyvianaki, Christoforos N. Hadjicostis, Themistoklis Charalambous, Karl H. Johansson
Date: 2023-04-02 00:00:00
Tasks: Distributed Optimization, Federated Learning, Quantization, Scheduling

We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation whereas the second one exhibits asynchronous operation. Both algorithms share salient features. Specifically, the algorithms operate exclusively with quantized values, which means that the information stored, processed and exchanged between neighboring nodes is subject to deterministic uniform quantization. The algorithms rely on event-driven updates in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage. Finally, once the algorithms converge, nodes distributively terminate their operation. We prove that our algorithms converge in a finite number of iterations to the exact optimal solution depending on the quantization level, and we present applications of our algorithms to (i) optimal task scheduling for data centers, and (ii) global model aggregation for distributed federated learning. We provide simulations of these applications to illustrate the operation, performance, and advantages of the proposed algorithms. Additionally, it is shown that our proposed algorithms compare favorably to algorithms in the current literature. Quantized communication and asynchronous updates increase the required time to completion, but finite-time operation is maintained.
On Degeneracy Issues in Multi-parametric Programming and Critical Region Exploration based Distributed Optimization in Smart Grid Operations
Authors: Haitian Liu, Ye Guo, Hao liu
Date: 2023-04-02 00:00:00
Tasks: Computational Efficiency, Distributed Optimization, Scheduling

Improving renewable energy resource utilization efficiency is crucial to reducing carbon emissions, and multi-parametric programming has provided a systematic perspective in conducting analysis and optimization toward this goal in smart grid operations. This paper focuses on two aspects of interest related to multi-parametric linear/quadratic programming (mpLP/QP). First, we study degeneracy issues of mpLP/QP. A novel approach to deal with degeneracies is proposed to find all critical regions containing the given parameter. Our method leverages properties of the multi-parametric linear complementary problem, vertex searching technique, and complementary basis enumeration. Second, an improved critical region exploration (CRE) method to solve distributed LP/QP is proposed under a general mpLP/QP-based formulation. The improved CRE incorporates the proposed approach to handle degeneracies. A cutting plane update and an adaptive stepsize scheme are also integrated to accelerate convergence under different problem settings. The computational efficiency is verified on multi-area tie-line scheduling problems with various testing benchmarks and initial states.
Multi-Agent Reachability Calibration with Conformal Prediction
Authors: Anish Muthali, Haotian Shen, Sampada Deglurkar, Michael H. Lim, Rebecca Roelofs, Aleksandra Faust, Claire Tomlin
Date: 2023-04-02 00:00:00
Tasks: Autonomous Driving, Conformal Prediction, Prediction, quantile regression, regression, Trajectory Planning

We investigate methods to provide safety assurances for autonomous agents that incorporate predictions of other, uncontrolled agents' behavior into their own trajectory planning. Given a learning-based forecasting model that predicts agents' trajectories, we introduce a method for providing probabilistic assurances on the model's prediction error with calibrated confidence intervals. Through quantile regression, conformal prediction, and reachability analysis, our method generates probabilistically safe and dynamically feasible prediction sets. We showcase their utility in certifying the safety of planning algorithms, both in simulations using actual autonomous driving data and in an experiment with Boeing vehicles.
A Resilient Distributed Algorithm for Solving Linear Equations
Authors: Jingxuan Zhu, Alvaro Velasquez, Ji Liu
Date: 2023-04-01 00:00:00

This paper presents a resilient distributed algorithm for solving a system of linear algebraic equations over a multi-agent network in the presence of Byzantine agents capable of arbitrarily introducing untrustworthy information in communication. It is shown that the algorithm causes all non-Byzantine agents' states to converge to the same least squares solution exponentially fast, provided appropriate levels of graph redundancy and objective redundancy are established. An explicit convergence rate is also provided.
Universal approximation of flows of control systems by recurrent neural networks
Authors: Miguel Aguiar, Amritam Das, Karl H. Johansson
Date: 2023-04-01 00:00:00

We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.
On the impact of regularization in data-driven predictive control
Authors: Valentina Breschi, Alessandro Chiuso, Marco Fabris, Simone Formentin
Date: 2023-04-01 00:00:00
Tasks: Model Predictive Control

Model predictive control (MPC) is a control strategy widely used in industrial applications. However, its implementation typically requires a mathematical model of the system being controlled, which can be a time-consuming and expensive task. Data-driven predictive control (DDPC) methods offer an alternative approach that does not require an explicit mathematical model, but instead optimize the control policy directly from data. In this paper, we study the impact of two different regularization penalties on the closed-loop performance of a recently introduced data-driven method called $\gamma$-DDPC. Moreover, we discuss the tuning of the related coefficients in different data and noise scenarios, to provide some guidelines for the end user.
Gaussian Mechanism Design for Prescribed Privacy Sets in Data Releasing Systems
Authors: Teimour Hosseinalizadeh, Nima Monshizadeh
Date: 2023-04-01 00:00:00

The data transmitted by cyber-physical systems can be intercepted and exploited by malicious individuals to infer privacy-sensitive information regarding the physical system. This motivates us to study the problem of preserving privacy in data releasing of linear dynamical system using stochastic perturbation. In this study, the privacy sensitive quantity is the initial state value of the system. For protecting its privacy, we directly design the covariance matrix of a Gaussian output noise to achieve a prescribed uncertainty set in the form of hyper-ellipsoids. This is done by correlated noise and through a convex optimization problem by considering the utility of released signals. Compared to other available methods, our proposed technique for designing the Gaussian output noise provides enhanced flexibility for system designers. As a case study, the results are applied to a heating ventilation and air conditioning system.
How Does Driver Non-compliance Destroy Traffic Routing Control?
Authors: Yu Tang, Li Jin, Kaan Ozbay
Date: 2023-04-01 00:00:00
Tasks: Management

Routing control is one of important traffic management strategies against urban congestion. However, it could be compromised by heterogeneous driver non-compliance with routing instructions. In this article we model the compliance in a stochastic manner and investigate its impacts on routing control. We consider traffic routing for two parallel links. Particularly, we consider two scenarios: one ignores congestion spillback while the other one considers it. We formulate the problem as a non-linear Markov chain, given random compliance rates. Then we propose the stability and instability conditions to reveal when the routing is able or unable to stabilize the traffic. We show that for links without congestion spillback there exists a sufficient and necessary stability criterion. For links admiting congestion propagation, we present one stability condition and one instability condition. This stability conditions allow us to quantify the impacts of driver non-compliance on the two-link network in terms of throughput. Finally, we illustrate the results with a set of numerical examples.
Data-Driven Output Regulation using Single-Gain Tuning Regulators
Authors: Liangjie Chen, John W. Simpson-Porco
Date: 2023-03-31 00:00:00

Current approaches to data-driven control are geared towards optimal performance, and often integrate aspects of machine learning and large-scale convex optimization, leading to complex implementations. In many applications, it may be preferable to sacrifice performance to obtain significantly simpler controller designs. We focus here on the problem of output regulation for linear systems, and revisit the so-called tuning regulator of E. J. Davison as a minimal-order data-driven design for tracking and disturbance rejection. Our proposed modification of the tuning regulator relies only on samples of the open-loop plant frequency response for design, is tuned online by adjusting a single scalar gain, and comes with a guaranteed margin of stability; this provides a faithful extension of tuning procedures for SISO integral controllers to MIMO systems with mixed constant and harmonic disturbances. The results are illustrated via application to a four-tank water control process.
Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model
Authors: Yijun Xu, Marcos Netto, Lamine Mili
Date: 2023-03-31 00:00:00
Tasks: Computational Efficiency

We propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment the a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.
Robust Tracking Control for Nonlinear Systems: Performance optimization via extremum seeking
Authors: Jiapeng Xu, Ying Tan, Xiang Chen
Date: 2023-03-31 00:00:00

This paper presents a controller design and optimization framework for nonlinear dynamic systems to track a given reference signal in the presence of disturbances when the task is repeated over a finite-time interval. This novel framework mainly consists of two steps. The first step is to design a robust linear quadratic tracking controller based on the existing control structure with a Youla-type filter $\tilde Q$. Secondly, an extra degree of freedom: a parameterization in terms of $\tilde Q$, is added to this design framework. This extra design parameter is tuned iteratively from measured tracking cost function with the given disturbances and modeling uncertainties to achieve the best transient performance. The proposed method is validated with simulation placed on a Furuta inverted pendulum, showing significant tracking performance improvement.
A Data-Driven Approach for Inverse Optimal Control
Authors: Zihao Liang, Wenjian Hao, Shaoshuai Mou
Date: 2023-03-31 00:00:00

This paper proposes a data-driven, iterative approach for inverse optimal control (IOC), which aims to learn the objective function of a nonlinear optimal control system given its states and inputs. The approach solves the IOC problem in a challenging situation when the system dynamics is unknown. The key idea of the proposed approach comes from the deep Koopman representation of the unknown system, which employs a deep neural network to represent observables for the Koopman operator. By assuming the objective function to be learned is parameterized as a linear combination of features with unknown weights, the proposed approach for IOC is able to achieve a Koopman representation of the unknown dynamics and the unknown weights in objective function together. Simulation is provided to verify the proposed approach.
On stochastic MPC formulations with closed-loop guarantees: Analysis and a unifying framework
Authors: Johannes Köhler, Ferdinand Geuss, Melanie N. Zeilinger
Date: 2023-03-31 00:00:00
Tasks: Model Predictive Control

We investigate model predictive control (MPC) formulations for linear systems subject to i.i.d. stochastic disturbances with bounded support and chance constraints. Existing stochastic MPC formulations with closed-loop guarantees can be broadly classified in two separate frameworks: i) using robust techniques; ii) feasibility preserving algorithms. We investigate two particular MPC formulations representative for these two frameworks called robust-stochastic MPC and indirect feedback stochastic MPC. We provide a qualitative analysis, highlighting intrinsic limitations of both approaches in different edge cases. Then, we derive a unifying stochastic MPC framework that naturally includes these two formulations as limit cases. This qualitative analysis is complemented with numerical results, showcasing the advantages and limitations of each method.
Identification of Forced Oscillation Sources in Wind Farms using E-SINDy
Authors: K. Victor Sam Moses Babu, Pratyush Chakraborty, Mayukha Pal
Date: 2023-03-31 00:00:00

The rapid growth of wind power generation has led to increased interest in understanding and mitigating the adverse effects of wind turbine wakes and forced oscillations in wind farms. In this paper, we model a wind farm consisting of three wind turbines connected to a distribution system. Forced oscillations due to wind shear and tower shadow are injected into the system. If these oscillations are unchecked, they could pose a severe threat to the operation of the system and damage to the equipment. Identifying the source and frequency of forced oscillations in wind farms from measurement data is challenging. Thus, we propose a data-driven approach that discovers the underlying equations governing a nonlinear dynamical system from measured data using the Ensemble-Sparse Identification of Nonlinear Dynamics (E-SINDy) method. The results suggest that E-SINDy is a valuable tool for identifying sources of forced oscillations in wind farms and could facilitate the development of suitable control strategies to mitigate their negative impacts.
Data-driven Eigenstructure Assignment for Sparse Feedback Design
Authors: Federico Celi, Giacomo Baggio, Fabio Pasqualetti
Date: 2023-03-31 00:00:00

This paper presents a novel approach for solving the pole placement and eigenstructure assignment problems through data-driven methods. By using open-loop data alone, the paper shows that it is possible to characterize the allowable eigenvector subspaces, as well as the set of feedback gains that solve the pole placement problem. Additionally, the paper proposes a closed-form expression for the feedback gain that solves the eigenstructure assignment problem. Finally, the paper discusses a series of optimization problems aimed at finding sparse feedback gains for the pole placement problem.
Direct Data-Driven Computation of Polytopic Robust Control Invariant Sets and State-Feedback Controllers
Authors: Manas Mejari, Ankit Gupta
Date: 2023-03-31 00:00:00

This paper presents a direct data-driven approach for computing robust control invariant (RCI) sets and their associated state-feedback control laws for linear time-invariant systems affected by bounded disturbances. The proposed method utilizes a single state-input trajectory generated from the system, to compute a polytopic RCI set with a desired complexity and an invariance-inducing feedback controller, without the need to identify a model of the system. The problem is formulated in terms of a set of sufficient linear matrix inequality conditions that are then combined in a semi-definite program to maximize the volume of the RCI set while respecting the state and input constraints. We demonstrate through a numerical case study that the proposed data-driven approach can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed.
Status Updating under Partial Battery Knowledge in Energy Harvesting IoT Networks
Authors: Mohammad Hatami, Markus Leinonen, Marian Codreanu
Date: 2023-03-31 00:00:00
Tasks: Decision Making

We study status updating under inexact knowledge about the battery levels of the energy harvesting sensors in an IoT network, where users make on-demand requests to a cache-enabled edge node to send updates about various random processes monitored by the sensors. To serve the request(s), the edge node either commands the corresponding sensor to send an update or uses the aged data from the cache. We find a control policy that minimizes the average on-demand AoI subject to per-slot energy harvesting constraints under partial battery knowledge at the edge node. Namely, the edge node is informed about sensors' battery levels only via received status updates, leading to uncertainty about the battery levels for the decision-making. We model the problem as a POMDP which is then reformulated as an equivalent belief-MDP. The belief-MDP in its original form is difficult to solve due to the infinite belief space. However, by exploiting a specific pattern in the evolution of beliefs, we truncate the belief space and develop a dynamic programming algorithm to obtain an optimal policy. Moreover, we address a multi-sensor setup under a transmission limitation for which we develop an asymptotically optimal algorithm. Simulation results assess the performance of the proposed methods.
Potential detrimental effects of real-time route recommendations in traffic networks
Authors: Tommaso Toso, Alain Y. Kibangou, Paolo Frasca
Date: 2023-03-31 00:00:00

Navigation apps have become pervasive in providing real-time route recommendations to travelers willing to minimize their travel times. However, such technologies introduce new complexities, raising concerns about their overall impact on traffic networks. This paper focuses on evaluating the effect of navigation apps on traffic flows, particularly examining how real-time route recommendations influence network efficiency and congestion. Using a dynamical network flow model, we study traffic dynamics between an origin-destination pair, where a fraction of drivers follow app recommendations while others rely on fixed route preferences. By incorporating supply-demand mechanisms to account for capacity and volume constraints on routes, we uncover partial demand transfer, i.e., only a portion of the traffic demand is able to traverse the network, while the rest builds up congestion at the origin. We prove that the dynamics converges to a globally stable equilibrium and we provide a detailed analysis of this equilibrium when the choices of the informed drivers follow a logit model, correlating the emergence of partial demand transfer to the penetration rate of navigation apps among users.
Global Momentum Estimation of an Electric Power System
Authors: Angelo Maurizio Brambilla, Davide del Giudice, Daniele Linaro, Federico Bizzarri
Date: 2023-03-31 00:00:00

This work presents a technique to estimate on-line the global momentum of an electric power system. It exploits the footprint of the principal frequency system dynamics. Probing tones are injected by a grid-forming converter-interfaced generator and the speed of its virtual rotor is exploited to extrapolate the footprint. The proposed technique is entirely data driven and thus it does not need any model of the power system. We show that the proposed technique is adequate to accurately estimate the actual global momentum contributed by synchronous machines and provided by the controllers of converter-interfaced generators that emulate the behavior of synchronous machines. The technique is comprehensively tested on a modified version of the IEEE 39-BUS system and a dynamic version of the IEEE 118-BUS system, containing grid forming converter interfaced generators.
A Study of an Atomic Mobility Game With Uncertainty Under Prospect Theory
Authors: Ioannis Vasileios Chremos, Heeseung Bang, Aditya Dave, Viet-Anh Le, Andreas A. Malikopoulos
Date: 2023-03-31 00:00:00
Tasks: Decision Making

In this paper, we present a study of a mobility game with uncertainty in the decision-making of travelers and incorporate prospect theory to model travel behavior. We formulate a mobility game that models how travelers distribute their traffic flows in a transportation network with splittable traffic, utilizing the Bureau of Public Roads function to establish the relationship between traffic flow and travel time cost. Given the inherent non-linearities and complexity introduced by the uncertainties, we propose a smooth approximation function to estimate the prospect-theoretic cost functions. As part of our analysis, we characterize the best-fit parameters and derive an upper bound for the error. We then show the existence of an equilibrium and its its best-possible approximation.
Data-Driven Covariance Steering Control Design
Authors: Joshua Pilipovsky, Panagiotis Tsiotras
Date: 2023-03-30 00:00:00
Tasks: Steering Control

This paper studies the problem of steering the distribution of a linear time-invariant system from an initial normal distribution to a terminal normal distribution under no knowledge of the system dynamics. This data-driven control framework uses data collected from the input and the state and utilizes the seminal work by Willems et al. to construct a data-based parametrization of the mean and the covariance control problems. These problems are then solved to optimality as convex programs using standard techniques from the covariance control literature. We also discuss the equivalence of indirect and direct data-driven covariance steering designs, as well as a regularized version of the problem that provides a balance between the two. We illustrate the proposed framework through a set of randomized trials on a double integrator system and show that the results match up almost exactly with the corresponding model-based method in the noiseless case. We then analyze the robustness properties of the data-free and data-driven covariance steering methods and demonstrate the trade-offs between performance and optimality among these methods in the presence of data corrupted with exogenous noise.