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Saeed Ahmed

Publications and source records attributed to Saeed Ahmed.

17 recordsLinked to original sources
arXiv2026

Distributed Traffic State Estimation in Connected Vehicle and Roadside Infrastructure Networks

This paper proposes a distributed traffic state estimation framework that combines infrastructure sensors and connected vehicles as cooperative sensing nodes. Using Vehicle-to-Everything (V2X) communication, nearby nodes exchange local estimates and update them through a distributed Kalman filter designed for a second-order macroscopic traffic flow model. A consensus step fuses heterogeneous information across the network, while projection steps enforce physically consistent traffic states. We evaluate the method on HighD and NGSIM data, and on microscopic SUMO simulations that capture transient congestion. The results show accurate reconstruction of highway traffic states and detection of nonlinear shockwave dynamics, even with sparse infrastructure sensing and intermittent vehicular connectivity. A statistical analysis further shows how CV penetration rate, V2X communication range, and infrastructure deployment affect estimation accuracy. In particular, with 10% CV penetration, V2X ranges of 300-400 m, and sparse infrastructure deployment, the combined infrastructure-vehicle configuration consistently outperforms approaches that rely only on infrastructure or only on connected vehicles.

eess.SY↗
arXiv2026

A Distributionally Robust Multi-agent Reinforcement Learning Framework for Intelligent Intersection Control

Multi-agent reinforcement learning (MARL) has emerged as a promising approach for traffic signal control. However, standard MARL policies typically optimize for expected returns under nominal conditions, leaving them highly vulnerable to spatial-temporal demand shifts and catastrophic congestion under adverse scenarios. To address this critical limitation, this paper proposes an algorithm-agnostic Distributionally Robust (DR) MARL framework integrating an adaptive Contextual-Bandit Worst-Case Estimator (CB-WCE). Operating on a slower timescale, the CB-WCE co-evolves with the traffic controllers by dynamically generating adversarial demand mixtures during training. This steers the learning process to fortify policies against bottleneck scenarios without requiring modifications to the underlying MARL architectures. The framework is evaluated across value-based, actor-critic, and policy-gradient methods on both a synthetic 5x5 grid and a heterogeneous Monaco City network. Empirical results demonstrate that the DR framework prevents unbounded queue growth and profoundly enhances both worst-case robustness and average-case efficiency. Notably, for the Proximal Policy Optimization (PPO) architecture in the Monaco environment, on average, robust retraining reduced the worst-case queue length by 74.39% and improved the average-case network-wide queue length by 75.45%. Furthermore, the retrained policies exhibit strong zero-shot generalization to unseen traffic distributions, highlighting the framework's scalability and potential for resilient real-world urban deployment.

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arXiv2026

A novel switched systems approach to nonconvex optimisation

We develop a novel switching dynamics that converges to the Karush-Kuhn-Tucker (KKT) point of a nonlinear optimisation problem. This new approach is particularly notable for its lower dimensionality compared to conventional primal-dual dynamics, as it focuses exclusively on estimating the primal variable. Our method is successfully illustrated on general quadratic optimisation problems, the minimisation of the classical Rosenbrock function, and a nonconvex optimisation problem stemming from the control of energy-efficient buildings.

math.OC↗
arXiv2025

Distributionally Robust Multi-Agent Reinforcement Learning for Intelligent Traffic Control

Learning-based traffic signal control is typically optimized for average performance under a few nominal demand patterns, which can result in poor behavior under atypical traffic conditions. To address this, we develop a distributionally robust multi-agent reinforcement learning framework for signal control on a 3x3 urban grid calibrated from a contiguous 3x3 subarea of central Athens covered by the pNEUMA trajectory dataset (Barmpounakis and Geroliminis, 2020). Our approach proceeds in three stages. First, we train a baseline multi-agent RL controller in which each intersection is governed by a proximal policy optimization agent with discrete signal phases, using a centralized training, decentralized execution paradigm. Second, to capture demand uncertainty, we construct eight heterogeneous origin-destination-based traffic scenarios-one directly derived from pNEUMA and seven synthetically generated-to span a wide range of spatial and temporal demand patterns. Over this scenario set, we train a contextual-bandit worst-case estimator that assigns mixture weights to estimate adversarial demand distributions conditioned on context. Finally, without modifying the controller architecture, we fine-tune the baseline multi-agent reinforcement learning agents under these estimated worst-case mixtures to obtain a distributionally robust multi-agent reinforcement learning controller. Across all eight scenarios, as well as on an unseen validation network based on the Sioux Falls configuration, the distributionally robust multi-agent reinforcement learning controller consistently reduces horizon-averaged queues and increases average speeds relative to the baseline, achieving up to 51% shorter queues and 38% higher speeds on the worst-performing scenarios.

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arXiv2025

Distributed Traffic State Estimation in V2X-Enabled Connected Vehicle Networks

This paper presents a distributed traffic state estimation framework in which infrastructure sensors and connected vehicles act as autonomous, cooperative sensing nodes. These nodes share local traffic estimates with nearby nodes using Vehicle-to-Everything (V2X) communication. The proposed estimation algorithm uses a distributed Kalman filter tailored to a second-order macroscopic traffic flow model. To achieve global state awareness, the algorithm employs a consensus protocol to fuse heterogeneous spatiotemporal estimates from V2X neighbors and applies explicit projection steps to maintain physical consistency in density and flow estimates. The algorithm's performance is validated through microscopic simulations of a highway segment experiencing transient congestion. Results demonstrate that the proposed distributed estimator accurately reconstructs nonlinear shockwave dynamics, even with sparse infrastructure sensors and intermittent vehicular network connectivity. Statistical analysis explores how different connected vehicle penetration rates affect estimation accuracy, revealing notable phase transitions in network observability.

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arXiv2025

Some dynamical properties of constrained Modified Swift-Hohenberg Equation

In this paper, we have studied the long-term behavior for the projected deterministic constrained modified Swift-Hohenberg equation with constraints and Dirichlet boundary conditions. Specifically, using Lojasiewicz-Simon inequality, we have shown that the global solution approaches an equilibrium state. Also, we have analyzed the rate at which the solution approaches equilibrium. Finally, we have proven the existence of a global attractor.

math.AP↗
arXiv2025

On the Global solution and Invariance of stochastic constrained Modified Swift-Hohenberg Equation on a Hilbert manifold

This paper aims to investigate the stochastic generalization of the projected deterministic constrained modified Swift-Hohenberg equation. In particular, we prove the global well-posedness and its invariance of Hilbert submanifold i.e. if the initial condition are chosen from submanifold then trajectories of solutions are going to stay on manifold. The proof of global well-posedness is based on Khashminskii test for non-explosions test for no-explosions. Swift-Hohenberg equations belong to class of Amplitude equations that usually describe the pattern formation in nature.

math.PR↗
arXiv2025

On the Global Solution and Invariance of nonlinear Constrained Modified Swift-Hohenberg Equation on Hilbert Manifold

In this paper, we are interested in proving the existence and uniqueness of the local, local maximal, and global solutions of the equation projected on the Hilbert manifold. Furthermore, we show that, for any given initial data in the Hilbert manifold $\mathcal{M}$, the solution to this equation is also in the Hilbert manifold $\mathcal{M}$. Finally, we demonstrate that the solution to the equation is a gradient flow.

math.DG↗
arXiv2025

Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation

In this paper, we aim to prove the existence of global Martingale solution to Stochastic Constrained Modified Swift-Hohenberg Equation driven by stratonovich multiplicative noise. This equation belongs to class of amplitude equations which describe the appearance of pattern formation in nature. This structure allows us to work in a Hilbert space framework and to apply a stochastic Galerkin method. The existence proof is based on energy-type estimates, the tightness criterion of Brzezniak and collaborators, and Jakubowski's generalization of the Skorokhod theorem.

math.PR↗
arXiv2025

Distributed Prescribed-Time Observer for Nonlinear Systems in Block-Triangular Form

This paper proposes a distributed prescribed-time observer for nonlinear systems representable in a block-triangular observable canonical form. Using a weighted average of neighbor estimates exchanged over a strongly connected digraph, each observer estimates the system state despite the limited observability of local sensor measurements. The proposed design guarantees that distributed state estimation errors converge to zero at a user-specified convergence time, irrespective of observers' initial conditions. To achieve this prescribed-time convergence, distributed observers implement time-varying local output injection gains that monotonically increase and approach infinity at the prescribed time. The theoretical convergence is rigorously proven and validated through numerical simulations, where some implementation issues due to increasing gains have also been clarified.

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arXiv2025

Economic Nonlinear Model Predictive Control of Prosumer District Heating Networks: The Extended Version

In this paper, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are essential components of 4th generation DHNs. These networks are characterized by their ability to optimize their operations, aiming to reduce supply temperatures, accommodate distributed heat sources, and leverage the flexibility provided by thermal inertia and storage, all crucial for achieving a fossil-fuel-free energy supply. Developing a smart energy management system to accomplish these goals requires detailed models of highly complex nonlinear systems and computational algorithms able to handle large-scale optimization problems. To address this, we introduce a graph-based optimization-oriented model that efficiently integrates distributed producers, prosumers, storage buffers, and bidirectional pipe flows, such that it can be implemented in a real-time MPC setting. Furthermore, we conduct several numerical experiments to evaluate the performance of the proposed algorithms in closed-loop. Our findings demonstrate that the MPC methods achieved up to 9% cost improvement over traditional rule-based controllers while better maintaining system constraints.

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arXiv2024

Existence of Martingale Solutions to Stochastic Constrained Heat Equation

This article extends the work on stochastic constrained heat equation in \cite{brzezniak2020global}. We will show the existence of Martingale solutions to the stochastic-constrained heat equations. The proof is based on compactness, tightness of measure, quadratic variations, and Martingale representation theorem.

math.PR↗
arXiv2024

Lyapunov Characterization for ISS of Impulsive Switched Systems

In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS conditions, we propose two types of time-varying ISS-Lyapunov functions: one that is non-decreasing and another one that is decreasing. Our research proves that the existence of either of these ISS-Lyapunov functions is a necessary and sufficient condition for ISS. We also present a technique for constructing a decreasing ISS-Lyapunov function from a non-decreasing one, which is useful for its own sake. Our findings also have added value to previous research that only studied sufficient conditions for ISS, as our results apply to a broader class of systems. This is because we impose less restrictive dwell and leave time constraints on the switching signal and our ISS-Lyapunov functions are time-varying with general nonlinear conditions imposed on them. Moreover, we provide a method to guarantee the ISS of a particular class of impulsive switched systems when the switching signal is unknown.

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arXiv2022

Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems

Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.

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arXiv2020

On Output Feedback Stabilization of Time-Varying Decomposable Systems with Switching Topology and Delay

This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems with switching topology as equivalent LPV systems with a piecewise constant parameter. In the second step, we design stabilizing output feedbacks for these LPV systems in the presence of a time-varying output delay using a trajectory-based stability analysis approach. We do not impose any constraint on the delay derivative. Finally, we illustrate our approach by applying it to the consensus problem of non-holonomic agents.

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arXiv2020

Dwell-Time Based Stability Analysis and L2 Control of LPV Systems with Piecewise Constant Parameters and Delay

Dwell-time based stability conditions for a class of LPV systems with piecewise constant parameters under time-varying delay are derived using clock-dependent Lyapunov-Krasovskii functional. Sufficient synthesis conditions for clock-dependent gain-scheduled state-feedback controllers ensuring L2-performance are also provided. Several numerical and practical examples, to illustrate the efficacy of the results, are given.

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