arXiv subjects

Mahdieh Zaker

Publications and source records attributed to Mahdieh Zaker.

11 recordsLinked to original sources

arXiv2026

Data-Driven Stabilizing Controller Design for Linear Infinite Networks

We propose a direct data-driven method for controller synthesis of infinite networks composed of unknown linear time-invariant subsystems. Using a single set of noise-corrupted input-state trajectories collected from each subsystem, and provided that certain linear matrix inequalities hold, each subsystem is rendered exponentially input-to-state stable (eISS) by locally constructing an eISS control Lyapunov function together with an exponentially input-to-state stabilizing feedback controller. We then compose these local components under a compositional small-gain condition in infinite-dimensional spaces to obtain a global control Lyapunov function and an associated stabilizing controller, ensuring uniform global exponential stability of the infinite network. The approach is validated on a physical case study with unknown dynamics.

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arXiv2026

Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies

Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, for which no fixed upper bound on the number of participating subsystems is specified a priori since it may vary over time as agents join or leave (e.g., vehicles in traffic). In such scenarios, the presence of infinitely many subsystems within the network renders the existing analysis frameworks tailored for finite networks inapplicable to infinite ones. This paper is concerned with offering a data-driven approach, within a compositional framework, for the safety certification of infinite networks with both unknown mathematical models and unknown interconnection topologies. Given the immense computational complexity stemming from the extensive dimension of infinite networks, our approach capitalizes on the joint dissipativity-type properties of subsystems, characterized by storage certificates. We introduce innovative compositional data-driven conditions to construct a barrier certificate for the infinite network leveraging storage certificates of its unknown subsystems derived from data, while offering correctness guarantees for network safety. We demonstrate that our compositional data-driven reasoning eliminates the requirement for checking the traditional dissipativity condition, which typically mandates precise knowledge of the interconnection topology. We illustrate our data-driven results on two physical infinite networks with unknown models and interconnection topologies.

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arXiv2026

Data-Driven Incremental GAS Certificate of Nonlinear Homogeneous Networks: A Scenario Approach with Noisy Data

This work focuses on a compositional data-driven approach to verify incremental global asymptotic stability (delta-GAS) over interconnected homogeneous networks of degree one with unknown mathematical dynamics. Our proposed approach leverages the concept of incremental input-to-state stability (delta-ISS) of subsystems, characterized by delta-ISS Lyapunov functions. To implement our data-driven scheme, we initially reframe the delta-ISS Lyapunov conditions as a robust optimization program (ROP). Due to the presence of unknown subsystem dynamics in the ROP constraints, we develop a scenario optimization program (SOP) by gathering data from trajectories of each unknown subsystem. However, since the measured one-step transition data are corrupted by noise with a known bound on its norm, rendering the proposed SOP intractable, we introduce an auxiliary SOP that explicitly accommodates noisy measurements. We solve the auxiliary SOP and construct a delta-ISS Lyapunov function for each subsystem with unknown dynamics. We then leverage a small-gain compositional condition to facilitate the construction of an incremental Lyapunov function for an unknown interconnected network based on the data-driven delta-ISS Lyapunov functions of its individual subsystems, while providing correctness guarantees, incorporating the bound on the noise norm. We demonstrate that our data-driven compositional approach reduces the sample complexity to the subsystem level. To validate the effectiveness of our approach, we apply it to an unknown controlled physical nonlinear homogeneous network of degree one, comprising 10000 subsystems. By gathering noisy data from each unknown subsystem, we demonstrate that the interconnected network is delta-GAS with a correctness guarantee.

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arXiv2026

Compositional Design of Safety Controllers for Large-Scale Stochastic Hybrid Systems

In this work, we propose a compositional scheme based on small-gain reasoning to synthesize safety controllers for interconnected stochastic hybrid systems. In our proposed setting, we first offer an augmented scheme that characterizes each stochastic hybrid subsystem, endowed with both continuous evolution and instantaneous jumps, within a unified framework including both scenarios, implying that its state trajectories coincide with those of the original hybrid subsystem. We then introduce the concept of augmented control sub-barrier certificates (A-CSBCs) for each subsystem, thereby enabling the construction of an augmented control barrier certificate (A-CBC) for an interconnected network (from A-CSBCs of its subsystems) along with its safety controller under small-gain compositional conditions. We eventually leverage the constructed A-CBC to derive a guaranteed lower bound on the safety probability of the interconnected network. While in a monolithic scheme the computational complexity of synthesizing a control barrier certificate via sum-of-squares (SOS) optimization scales polynomially with the overall network size, the proposed compositional framework reduces this dependence to the subsystem size. We illustrate the efficacy of the proposed approach on an interconnected network comprising 1000 stochastic hybrid subsystems with nonlinear dynamics under two distinct interconnection topologies.

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arXiv2026

Data-Driven Global Stabilization of Unknown Infinite Networks

This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS). To address scalability challenges arising from high dimensionality, we develop a data-driven approach to construct an input-to-state stable (ISS) Lyapunov function and its corresponding controller for each unknown subsystem using only a single set of noise-corrupted input-state trajectories collected from that subsystem. Once each subsystem admits a data-driven ISS Lyapunov function, we leverage a compositional small-gain framework for infinite-dimensional spaces to construct a global control Lyapunov function and its associated controller, thereby ensuring UGAS of the entire infinite network. The effectiveness of the proposed data-driven approach is demonstrated through three case studies, including infinite networks of spacecraft, Lorenz chaotic systems, and an academic example with a state-dependent control input matrix.

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arXiv2025

Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics

Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical applications where input precision cannot be guaranteed. However, analyzing delta-ISS demands precise knowledge of system dynamics to assess the state's incremental response to input changes, posing a challenge in real-world scenarios where mathematical models are unknown. In this work, we develop a data-driven approach to design delta-ISS Lyapunov functions together with their corresponding delta-ISS controllers for continuous-time input-affine nonlinear systems with polynomial dynamics, ensuring the delta-ISS property is achieved without requiring knowledge of the system dynamics. In our data-driven scheme, we collect only two sets of input-state trajectories from sufficiently excited dynamics. By fulfilling a specific rank condition, we design delta-ISS controllers using the collected samples through formulating a sum-of-squares optimization program. The effectiveness of our data-driven approach is evidenced by its application to a physical case study.

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arXiv2025

ARCH-COMP25 Category Report: Stochastic Models

This report is concerned with a friendly competition for formal verification and policy synthesis of stochastic models. The main goal of the report is to introduce new benchmarks and their properties within this category and recommend next steps toward next year's edition of the competition. In particular, this report introduces three recently developed software tools, a new water distribution network benchmark, and a collection of simplified benchmarks intended to facilitate further comparisons among tools that were previously not directly comparable. This friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Summer 2025.

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arXiv2025

From Data to Global Asymptotic Stability of Unknown Large-Scale Networks with Provable Guarantees

We offer a compositional data-driven scheme for synthesizing controllers that ensure global asymptotic stability (GAS) across large-scale interconnected networks, characterized by unknown mathematical models. In light of each network's configuration composed of numerous subsystems with smaller dimensions, our proposed framework gathers data from each subsystem's trajectory, enabling the design of local controllers that ensure input-to-state stability (ISS) properties over subsystems, signified by ISS Lyapunov functions. To accomplish this, we require only a single input-state trajectory from each unknown subsystem up to a specified time horizon, fulfilling certain rank conditions. Subsequently, under small-gain compositional reasoning, we leverage ISS Lyapunov functions derived from data to offer a control Lyapunov function (CLF) for the interconnected network, ensuring GAS certificate over the network. We demonstrate that while the computational complexity for designing a CLF increases polynomially with the network dimension using sum-of-squares (SOS) optimization, our compositional data-driven approach significantly mitigates it to \emph{linear} with respect to the number of subsystems. We showcase the efficacy of our data-driven approach over a set of benchmarks, involving physical networks with diverse interconnection topologies.

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arXiv2024

Abstraction-based Control of Unknown Continuous-Space Models with Just Two Trajectories

Finite abstractions (a.k.a. symbolic models) offer an effective scheme for approximating the complex continuous-space systems with simpler models in the discrete-space domain. A crucial aspect, however, is to establish a formal relation between the original system and its symbolic model, ensuring that a discrete controller designed for the symbolic model can be effectively implemented as a hybrid controller (using an interface map) for the original system. This task becomes even more challenging when the exact mathematical model of the continuous-space system is unknown. To address this, the existing literature mainly employs scenario-based data-driven methods, which require collecting a large amount of data from the original system. In this work, we propose a data-driven framework that utilizes only two input-state trajectories collected from unknown nonlinear polynomial systems to synthesize a hybrid controller, enabling the desired behavior on the unknown system through the controller derived from its symbolic model. To accomplish this, we employ the concept of alternating simulation functions (ASFs) to quantify the closeness between the state trajectories of the unknown system and its data-driven symbolic model. By satisfying a specific rank condition on the collected data, which intuitively ensures that the unknown system is persistently excited, we directly design an ASF and its corresponding hybrid controller using finite-length data without explicitly identifying the unknown system, while providing correctness guarantees. This is achieved through proposing a data-based sum-of-squares (SOS) optimization program, enabling a systematic approach to the design process. We illustrate the effectiveness of our data-driven approach through a case study.

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arXiv2024

From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems

This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing system safety over an infinite time horizon. The proposed approach leverages measured data acquired through an input-output observation, referred to as a single trajectory, collected over a specified time horizon. By fulfilling a certain rank condition, which ensures the unknown system is persistently excited by the collected data, we design a CBC and its corresponding safety controller directly from the finite-length observed data, without explicitly identifying the unknown dynamical system. This is achieved through proposing a data-based sum-of-squares optimization (SOS) program to systematically design CBCs and their safety controllers. We validate our data-driven approach over two physical case studies including a jet engine and a Lorenz system, demonstrating the efficacy of our proposed method.

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arXiv2024

Rare Collision Risk Estimation of Autonomous Vehicles with Multi-Agent Situation Awareness

This paper offers a formal framework for the rare collision risk estimation of autonomous vehicles (AVs) with multi-agent situation awareness, affected by different sources of noise in a complex dynamic environment. In our proposed setting, the situation awareness is considered for one of the ego vehicles by aggregating a range of diverse information gathered from other vehicles into a vector. We model AVs equipped with the situation awareness as general stochastic hybrid systems (GSHS) and assess the probability of collision in a lane-change scenario where two self-driving vehicles simultaneously intend to switch lanes into a shared one, while utilizing the time-to-collision measure for decision-making as required. Due to the substantial data requirements of simulation-based methods for the rare collision risk estimation, we leverage a multi-level importance splitting technique, known as interacting particle system-based estimation with fixed assignment splitting (IPS-FAS). This approach allows us to estimate the probability of a rare event by employing a group of interacting particles. Specifically, each particle embodies a system trajectory and engages with others through resampling and branching, focusing computational resources on trajectories with the highest probability of encountering the rare event. The effectiveness of our proposed approach is demonstrated through an extensive simulation of a lane-change scenario.

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