arXiv subjects

MirSaleh Bahavarnia

Publications and source records attributed to MirSaleh Bahavarnia.

16 recordsLinked to original sources

arXiv2026

Stabilizing Traffic Flow Via Autonomous Vehicles: A Less Conservative Approach

This paper explores stabilizing traffic flow using a minimum number of autonomous vehicles (AVs) under control constraints. In contrast to most studies, we consider a heterogeneous parameter setup scenario for human-driven vehicles (HVs) to reflect real-world differences in driving behavior. While current literature uses an H-Infinity based sufficient condition to ensure the string stability of traffic flow, this often yields a conservative lower bound on the AV penetration rate to stabilize traffic flow. To reduce such conservativeness and obtain a less conservative lower bound, we ensure the string stability of traffic flow by directly imposing the possession of no growing eigenmodes. We also systematically find a minimum number of required AVs and solve for the optimal control parameters via nonlinear optimization. We finally assess the intended conservativeness reduction via numerical simulations. Quantitatively, applying our algorithm to the homogeneous HV baseline in the literature (the result built upon an H-Infinity based sufficient condition) reduces (improves) the AV penetration rate by 17.14% while ensuring the string stability of traffic flow. We observe a trade-off between the stabilization/performance degradation and the number of utilized identical AVs. Quantitatively, our last numerical simulation corroborates that the AV penetration rate can be reduced by 61.54% at the expense of 27.66% higher position difference deviation from the equilibrium and a 92.47% degradation in the real stability radius (RSR)---a metric to measure the stability robustness under the perturbation/uncertainty---associated with the aggregated linearized dynamics while ensuring the string stability of traffic flow. This trade-off helps engineers/operators make better traffic control decisions.

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arXiv2026

Dynamic Centrality Measures for Water Distribution Network Hydraulics

Water distribution networks (WDNs) are susceptible to various failures, including but not limited to human errors, cyber-attacks, and network modifications, necessitating the vulnerability analysis of WDNs. Graph-theoretic centrality measures---as a main class of centrality measures---aim to rank the network components solely based on their influence (i.e., criticality) on the WDN topology in the case of input changes, while overlooking the WDN dynamics. To overcome such a limitation, this paper uses a control-theoretic centrality measure to identify the network's most and least influential pipes in WDNs, by simultaneously incorporating the dynamics and topology of the WDN. First, given a WDN modeled by nonlinear differential-algebraic equations (NDAEs) consisting of transient flow dynamics as differential equation (DE) and conservation of water mass as algebraic equation (AE) and considering the pipe flow rates as states of the state-space (SS) representation, we extract a linearized system modeled by linear ordinary differential equations (LODEs) around the equilibrium (i.e., steady) flow rate vector. Second, treating pipe flow rates as SS nodes (states), we introduce a node centrality-based measure, namely \textit{vulnerability vector (VV)}, to rank the network pipes based on their influence on the dynamics and topology of the WDN in the case of input changes. In particular, the network's most and least influential pipes can be identified through such a centrality-based approach. This enables water engineers to understand the WDN's vulnerability better and effectively prioritize the maintenance and operational efforts on the most influential pipes within the WDN.

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arXiv2026

A Bayesian Approach for the Network Reconstruction of Interdependent Critical Infrastructure Systems from Cascading Failures

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.

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arXiv2025

Quick Updates for the Perturbed Static Output Feedback Control Problem in Linear Systems with Applications to Power Systems

This paper introduces a method for efficiently updating a nominal stabilizing static output feedback (SOF) controller in perturbed linear systems. As operating points and state-space matrices change in dynamic systems, accommodating updates to the SOF controller are necessary. Traditional methods address such changes by re-solving for the updated SOF gain, which is often (i) computationally expensive due to the NP-hard nature of the problem or (ii) infeasible due to the limitations of its semidefinite programming relaxations. To overcome this, we leverage the concept of minimum destabilizing real perturbation (MDRP) to formulate a norm minimization problem that yields fast, reliable controller updates. This approach accommodates a variety of known perturbations, including abrupt changes, model inaccuracies, and equilibrium-dependent linearizations. We remark that the application of our proposed approach is limited to the class of SOF controllers in perturbed linear systems. We also introduce geometric metrics to quantify the proximity to instability and rigorously define stability-guaranteed regions. Extensive numerical simulations validate the efficiency and robustness of the proposed method. Moreover, such extensive numerical simulations corroborate that although we utilize a heuristic optimization method to compute the MDRP, it performs quite well in practice compared to an existing approximation method in the literature, namely the hybrid expansion-contraction (HEC) method. We demonstrate the results on the SOF control of multi-machine power networks with changing operating points, and demonstrate that the computed quick updates produce comparable solutions to the traditional SOF ones, while requiring orders of magnitude less computational time.

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arXiv2025

Wide-Area Feedback Control for Renewables-Heavy Power Systems: A Comparative Study of Reinforcement Learning and Lyapunov-Based Design

As renewable energy sources become more prevalent, accurately modeling power grid dynamics is becoming increasingly more complex. Concurrently, data acquisition and realtime system state monitoring are becoming more available for control centers. This motivates shifting from \textit{model- and Lyapunov-based} feedback controller designs toward \textit{model-free} ones. Reinforcement learning (RL) has emerged as a key tool for designing model-free controllers. Various studies have been carried out to study voltage/frequency control strategies via RL. However, usually a simplified system model is used neglecting detailed dynamics of solar, wind, and composite loads -- and damping system-wide oscillations and modeling power flows are all usually ignored. To that end, we pose an optimal feedback control problem for a detailed renewables-heavy power system, defined by a set of nonlinear differential algebraic equations (NDAE). The control problem is solved using a completely model-free design via RL as well as using a model-based approach built upon the Lyapunov stability theory with guarantees. The paper in its essence seeks to explore whether data-driven feedback control should be used in power grids over its model-driven counterpart. Theoretical developments and thorough case studies are presented with an eye on this exploration. Finally, a detailed analysis is provided to delineate the strengths and weaknesses of both approaches for renewables-heavy grids.

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arXiv2025

Improving Power Systems Controllability via Edge Centrality Measures

Improving the controllability of power networks is crucial as they are highly complex networks operating in synchrony; even minor perturbations can cause desynchronization and instability. To that end, one needs to assess the criticality of key network components (buses and lines) in terms of their impact on system performance. Traditional methods to identify the key nodes/edges in power networks often rely on static centrality measures based on the network's topological structure ignoring the network's dynamic behavior. In this paper, using multi-machine power network models and a new control-theoretic edge centrality matrix (ECM) approach, we: (i) quantify the influence of edges (i.e., the line susceptances) in terms of controllability performance metrics, (ii) identify the most influential lines, and (iii) compute near-optimal edge modifications that improve the power network controllability. Employing various IEEE power network benchmarks, we validate the effectiveness of the ECM-based algorithm and demonstrate improvements in system reachability, control, and damping performance.

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arXiv2024

How many autonomous vehicles are required to stabilize traffic flow?

The collective behavior of human-driven vehicles (HVs) produces the well-known stop-and-go waves potentially leading to higher fuel consumption and emissions. This paper investigates the stabilization of traffic flow via a minimum number of autonomous vehicles (AVs) subject to constraints on the control parameters aiming to reduce the number of vehicles on the road while achieving lower fuel consumption and emissions. The unconstrained scenario has been well-studied in recent studies. The main motivation to investigate the constrained scenario is that, in realistic engineering applications, lower and upper bounds exist on the control parameters. For the constrained scenario, we optimally find the minimum number of required AVs (via computing the optimal lower bound on the AV penetration rate) to stabilize traffic flow for a given number of HVs. As an immediate consequence, we conclude that for a given number of AVs, the number of HVs in the stabilized traffic flow may not be arbitrarily large in the constrained scenario unlike the unconstrained scenario studied in the literature. We systematically propose a procedure to compute the optimal lower bound on the AV penetration rate using nonlinear optimization techniques. Finally, we validate the theoretical results via numerical simulations. Numerical simulations suggest that enlarging the constraint intervals makes a smaller optimal lower bound on the AV penetration rate attainable. However, it leads to a slower transient response due to a dominant pole closer to the origin.

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arXiv2024

On the Constrained CAV Platoon Control Problem

The main objective of the connected and automated vehicle (CAV) platoon control problem is to regulate CAVs' position while ensuring stability and accounting for vehicle dynamics. Although this problem has been studied in the literature, existing research has some limitations. This paper presents two new theoretical results that address these limitations: (i) the synthesis of unrealistic high-gain control parameters due to the lack of a systematic way to incorporate the lower and upper bounds on the control parameters, and (ii) the performance sensitivity to the communication delay due to inaccurate Taylor series approximation. To be more precise, taking advantage of the wellknown Pade approximation, this paper proposes a constrained CAV platoon controller synthesis that (i) systematically incorporates the lower and upper bounds on the control parameters, and (ii) significantly improves the performance sensitivity to the communication delay. The effectiveness of the presented results is verified through conducting extensive numerical simulations. The proposed controller effectively attenuates the stop-and-go disturbance -- a single cycle of deceleration followed by acceleration -- amplification throughout the mixed platoon (consisting of CAVs and human-driven vehicles). Modern transportation systems will benefit from the proposed CAV controls in terms of effective disturbance attenuation as it will potentially reduce collisions.

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arXiv2023

Learning for System Identification of NDAE-modeled Power Systems

System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by differential-algebraic equations (DAEs). This paper introduces a neural network (NN) framework for effectively learning and simulating solution trajectories of DAEs. The proposed framework leverages the synergy between Implicit Runge-Kutta (IRK) time-stepping schemes tailored for DAEs and NNs (including a differential NN (DNN)). The framework enforces an NN to cooperate with the algebraic equation of DAEs as hard constraints and is suitable for the identification of the ordinary differential equation (ODE)-modeled dynamic equation of DAEs using an existing penalty-based algorithm. Finally, the paper demonstrates the efficacy and precision of the proposed NN through the identification and simulation of solution trajectories for the considered DAE-modeled power system.

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arXiv2023

On Scaling Robust Feedback Control and State Estimation Problems in Power Networks

Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of scalability and sensitivity. In particular, Lyapunov-based approaches rely on forming semi-definite programs (SDPs) that are (i) not scalable and (ii) extremely sensitive to the choice of the bounding scalar that ensures the strict feasibility of the linear matrix inequalities (LMIs). This paper addresses these two issues by employing a celebrated non-Lyapunov approach (NLA) from the control theory literature. In lieu of linearized models of power grids, we focus on (the more representative) nonlinear differential algebraic equation (DAE) models and showcase the simplicity, scalability, and parameter-resiliency of NLA. For some power systems, the approach is nearly fifty times faster than solving SDPs via standard solvers with almost no impact on the performance. The case studies also demonstrate that NLA can be applied to more realistic scenarios in which (i) only partial state data is available and (ii) sparsity structures are imposed on the feedback gain. The paper also showcases that virtually no degradation in state estimation quality is experienced when applying NLA.

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arXiv2023

Robust Feedback Control of Power Systems with Solar Plants and Composite Loads

Due to the rapid developments in synchronized measurement technologies, there exist enormous opportunities to attenuate disturbances in future power grids with high penetration of renewables and complex load demands. To that end, this paper investigates the effectiveness of new robust feedback controllers for interconnected power systems with advanced power electronics-based models of photovoltaic (PV) power plants, composite load dynamics, and detailed higher-order synchronous generator models. Specifically, we design new, advanced control-theoretic wide-area controllers to improve the transient stability of nonlinear differential-algebraic models. Thorough simulation studies are carried out to assess the performance of the proposed controllers. Several fundamental questions on the proposed controllers' computational complexity and disturbance attenuation performance are raised and addressed. Simulation results demonstrate that with the proposed controllers as a secondary control layer, the overall transient stability and system robustness against load and renewables disturbances/uncertainties can be significantly improved compared to the state-of-the-art.

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arXiv2023

CAV Traffic Control to Mitigate the Impact of Congestion from Bottlenecks: A Linear Quadratic Regulator Approach and Microsimulation Study

This work investigates traffic control via controlled connected and automated vehicles (CAVs) using novel controllers derived from the linear-quadratic regulator (LQR) theory. CAV-platoons are modeled as moving bottlenecks impacting the surrounding traffic with their speeds as control inputs. An iterative controller algorithm based on the LQR theory is proposed along with a variant that allows for penalizing abrupt changes in platoons speeds. The controllers use the Lighthill-Whitham-Richards (LWR) model implemented using an extended cell transmission model (CTM) which considers the capacity drop phenomenon for a realistic representation of traffic in congestion. The impact of various parameters of the proposed controller on the control performance is analyzed. The effectiveness of the proposed traffic control algorithms is tested using a traffic control example and compared with existing proportional-integral (PI)- and model predictive control (MPC)- based controllers from the literature. A case study using the TransModeler traffic microsimulation software is conducted to test the usability of the proposed controller as well as existing controllers in a realistic setting and derive qualitative insights. It is observed that the proposed controller works well in both settings to mitigate the impact of the jam caused by a fixed bottleneck. The computation time required by the controller is also small making it suitable for real-time control.

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arXiv2019

Resilient Sparse Controller Design with Guaranteed Disturbance Attenuation

We design resilient sparse state-feedback controllers for a linear time-invariant (LTI) control system while attaining a pre-specified guarantee on ${\mathcal{H}}_\infty$ performance measure. We leverage a technique from non-fragile control theory to identify a region of resilient state-feedback controllers. Afterward, we explore the region to identify a sparse controller. To this end, we use two different techniques: the greedy method of sparsification, as well as the re-weighted $\ell_1$ norm minimization. Our approach highlights a tradeoff between the sparsity of the feedback gain, performance measure, and fragility of the design. To best of our knowledge, this work is the first framework providing performance guarantees for sparse feedback gain design.

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arXiv2018

Sparse Sensing, Communication, and Actuation via Self-Triggered Control Algorithms

We propose a self-triggered control algorithm to reduce onboard processor usage, communication bandwidth, and energy consumption across a linear time-invariant networked control system. We formulate an optimal control problem by penalizing the l0-measures of the feedback gain and the vector of control inputs and maximizing the dwell time between the consecutive triggering times. It is shown that the corresponding l1-relaxation of the optimal control problem is feasible and results in a stabilizing feedback control law with guaranteed performance bounds, while providing a sparse schedule for collecting samples from sensors, communication with other subsystems, and activating the input actuators.

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arXiv2018

Feedback Controller Sparsification for a Class of Linear Systems with Parametric Uncertainties

We consider the problem of output feedback controller sparsification for systems with parametric uncertainties. We develop an optimization scheme that minimizes the performance deterioration caused by the sparsification process, while enhancing sparsity pattern of the feedback gain. In order to improve temporal proximity of an existing closed-loop system and its sparsified counterpart, we also incorporate an additional constraint into the problem formulation so as to bound the variation in the system output pre and post sparsification. We also show that the resulting non-convex optimization problem can be equivalently reformulated into a rank-constrained optimization problem. We then formulate a bi-linear minimization program along with an iterative algorithm to obtain a sub-optimal solution which satisfies the rank constraint with arbitrary tolerance. Lastly, a sub-optimal sparse controller design for IEEE 39-bus New England power network is utilized to showcase the effectiveness of our proposed method.

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arXiv2015

Sparse Linear-Quadratic Feedback Design Using Affine Approximation

We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator (LQR) problem in order to promote sparsity pattern of the state feedback controller. This class of problems is generally NP hard and computationally intractable. First, we apply a $\ell_1$-relaxation and consider the $\ell_1$-regularized LQ version of this class of problems, which is still nonconvex. Then, we convexify the resulting $\ell_1$-regularized LQ problem by applying affine approximation techniques. An iterative algorithm is proposed to solve the $\ell_1$-regularized LQ problem using a series of convexified $\ell_1$-regularized LQ problems. By means of several numerical experiments, we show that our proposed algorithm is comparable to the existing algorithms in the literature, and in some cases it even returns solutions with superior performance and sparsity pattern.

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