arXiv subjects

Amy Nejati

Publications and source records attributed to Amy Nejati.

15 recordsLinked to original sources

arXiv2026

Data-Driven Formal Methods for Complex Dynamical Systems: A Survey

Data-driven approaches with formal guarantees have recently emerged as a powerful means for the verification and controller synthesis of complex dynamical systems. Interest in these methods is rapidly growing, as system models are often unavailable in practice, and challenges such as nonlinear behavior, uncertainty, and the curse of dimensionality typically render accurate modeling infeasible. These difficulties motivate leveraging limited data collected from the system while still providing formal guarantees on its overall behavior. The community has therefore proposed a few hundred articles on the development of data-driven frameworks that enable the formal verification and synthesis of dynamical systems without explicit models, addressing complex specifications beyond stability. Despite this rapid growth, existing results remain scattered and lack a coherent organization, limiting a clear understanding of their principles, distinctions, and practical potential. This survey fills this gap by providing a comprehensive overview of these data-driven methods for both deterministic and stochastic dynamical systems. We structure the literature around three main methodological pillars in formal methods: (in)finite-abstraction-based techniques, functional certificate approaches, such as control barrier certificates, and compositional methods. For each of these approaches, we classify the resulting data-driven guarantees into three main categories: (i) statistical guarantees grounded in probably approximately correct and scenario-based frameworks, (ii) guarantees derived from Lipschitz continuity, and (iii) guarantees exploiting structural properties. While the literature on deterministic systems is considerably richer, we also devote particular attention to the stochastic counterpart, highlighting the inherent differences and challenges that arise compared to the deterministic case.

eess.SY↗

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.

eess.SY↗

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.

eess.SY↗

arXiv2026

Safety Controller Synthesis for Stochastic Polynomial Time-Delayed Systems

This work develops a theoretical framework for safety controller synthesis in discrete-time stochastic nonlinear polynomial systems subject to time-invariant delays (dt-SNPS-td). While safety analysis of stochastic systems using control barrier certificates (CBC) has been widely studied, developing safety controllers for stochastic systems with time delays remains largely unexplored. The main challenge arises from the need to account for the influence of delayed components when formulating and enforcing safety conditions. To address this, we employ Krasovskii control barrier certificates, which extend the conventional CBC framework by augmenting it with an additional summation term that captures the influence of delayed states. This formulation integrates both the current and delayed components into a unified barrier structure, enabling safety synthesis for stochastic systems with time delays. The proposed approach synthesizes safety controllers under input constraints, offering probabilistic safety guarantees robust to such delays: it ensures that all trajectories of the dt-SNPS-td remain within the prescribed safe region while fulfilling a quantified probabilistic bound. To achieve this, our method reformulates the safety constraints as a sum-of-squares optimization program, enabling the systematic construction of Krasovskii CBC together with their associated safety controllers. We validate the proposed framework through three case studies, including two physical systems, demonstrating its effectiveness and practical applicability.

eess.SY↗

arXiv2026

A Data-Driven Krasovskii-Based Approach for Safety Controller Design of Time-Delayed Uncertain Polynomial Systems

We develop a data-driven framework for the synthesis of robust Krasovskii control barrier certificates (RK-CBC) and corresponding robust safety controllers (R-SC) for discrete-time input-affine uncertain polynomial systems with unknown dynamics, while explicitly accounting for unknown-but-bounded disturbances and time-invariant delays using only observed input-state data. Although control barrier certificates have been extensively studied for safety analysis of control systems, existing work on unknown systems with time delays, particularly in the presence of disturbances, remains limited. The challenge of safety synthesis for such systems stems from two main factors: first, the system's mathematical model is unavailable; and second, the safety conditions should explicitly incorporate the effects of time delays on system evolution during the synthesis process, while remaining robust to unknown disturbances. To address these challenges, we develop a data-driven framework based on Krasovskii control barrier certificates, extending the classical CBC formulation for delay-free systems to explicitly account for time delays by aggregating delayed components within the barrier construction. The proposed framework relies solely on input-state data collected over a finite time horizon, enabling the direct synthesis of RK-CBC and R-SC from observed trajectories without requiring an explicit system model. The synthesis is cast as a data-driven sum-of-squares (SOS) optimization program, yielding a structured design methodology. As a result, robust safety is guaranteed in the presence of unknown disturbances and time delays over an infinite time horizon. The effectiveness of the proposed method is demonstrated through three case studies, including two physical systems.

eess.SY↗

arXiv2025

From Formal Methods to Data-Driven Safety Certificates of Unknown Large-Scale Networks

In this work, we propose a data-driven scheme within a compositional framework with noisy data to design robust safety controllers in a fully decentralized fashion for large-scale interconnected networks with unknown mathematical dynamics. Despite the network's high dimensionality and the inherent complexity of its unknown model, which make it intractable, our approach effectively addresses these challenges by (i) treating the network as a composition of smaller subsystems, and (ii) collecting noisy data from each subsystem's trajectory to design a control sub-barrier certificate (CSBC) and its corresponding local controller. To achieve this, our proposed scheme only requires a noise-corrupted single input-state trajectory from each unknown subsystem up to a specified time horizon, satisfying a certain rank condition. Subsequently, under a small-gain compositional reasoning, we compose those CSBC, derived from noisy data, and formulate a control barrier certificate (CBC) for the unknown network, ensuring its safety over an infinite time horizon, while providing correctness guarantees. We offer a data-dependent sum-of-squares (SOS) optimization program for computing CSBC alongside local controllers of subsystems. We illustrate that while the computational complexity of designing a CBC and its safety controller grows polynomially with network dimension using SOS optimization, our compositional data-driven approach significantly reduces it to a linear scale concerning the number of subsystems. We demonstrate the capability of our data-driven approach on multiple physical networks involving unknown models and a range of interconnection topologies.

eess.SY↗

arXiv2025

Data-Efficient Control of Polynomial Systems via Physics-Guided Quadratic Constraints

This work addresses the critical challenge of guaranteeing safety for complex dynamical systems where precise mathematical models are uncertain and data measurements are corrupted by noise. We develop a physics-guided, direct data-driven framework for synthesizing robust safety controllers for discrete-time nonlinear polynomial systems that are subject to unknown-but-bounded disturbances. To do so, we introduce a notion of safety through robust control barrier certificates, which ensure avoidance of unsafe regions, offering a less conservative alternative to existing methods based on robust invariant sets. To achieve data efficiency, we further integrate physical information, formulated as quadratic constraints on system and control matrices, with observed noisy data. This integration drastically reduces data requirements, enabling robust safety analysis with significantly shorter trajectories compared to purely data-driven methods. The proposed synthesis procedure is formulated as a sum-of-squares optimization program that systematically designs the barrier and its associated controller by leveraging both collected data and underlying physical laws. The efficacy of our framework is demonstrated on three benchmark systems, confirming its ability to offer robust safety guarantees with reduced data demands.

eess.SY↗

arXiv2025

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.

eess.SY↗

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.

cs.LO↗

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.

eess.SY↗

arXiv2025

TRUST: Stability and Safety Controller Synthesis for Unknown Dynamical Models Using a Single Trajectory

TRUST is an open-source software tool developed for data-driven controller synthesis of dynamical systems with unknown mathematical models, ensuring either stability or safety properties. By collecting only a single input-state trajectory from the unknown system and satisfying a rank condition that ensures the system is persistently excited according to the Willems et al.'s fundamental lemma, TRUST aims to design either control Lyapunov functions (CLF) or control barrier certificates (CBC), along with their corresponding stability or safety controllers. The tool implements sum-of-squares (SOS) optimization programs solely based on data to enforce stability or safety properties across four system classes: (i) continuous-time nonlinear polynomial systems, (ii) continuous-time linear systems, (iii) discrete-time nonlinear polynomial systems, and (iv) discrete-time linear systems. TRUST is a Python-based web application featuring an intuitive, reactive graphic user interface (GUI) built with web technologies. It can be accessed at https://trust.tgo.dev or installed locally, and supports both manual data entry and data file uploads. Leveraging the power of the Python backend and a JavaScript frontend, TRUST is designed to be highly user-friendly and accessible across desktop, laptop, tablet, and mobile devices. We apply TRUST to a set of physical benchmarks with unknown dynamics, ensuring either stability or safety properties across the four supported classes of models.

eess.SY↗

arXiv2025

Model Order Reduction from Data with Certification

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for high-dimensional systems with complex behaviors can be challenging, rendering MOR a practical alternative to achieve results that closely resemble those of the original complex systems. To construct such effective reduced-order models (ROMs), existing literature generally necessitates precise knowledge of original systems, which is often unavailable in real-world scenarios. This paper introduces a data-driven scheme to construct ROMs of dynamical systems with unknown mathematical models. Our methodology leverages data and establishes similarity relations between output trajectories of unknown systems and their data-driven ROMs via the notion of simulation functions (SFs), capable of formally quantifying their closeness. To achieve this, under a rank condition readily fulfillable using data, we collect only two input-state trajectories from unknown systems to construct both ROMs and SFs, while offering correctness guarantees. We demonstrate that the proposed ROMs derived from data can be leveraged for controller synthesis endeavors while effectively ensuring high-level logic properties over unknown dynamical models. We showcase our data-driven findings across a range of benchmark scenarios involving various unknown physical systems, demonstrating the enforcement of diverse complex properties.

eess.SY↗

arXiv2024

A Physics-Informed Scenario Approach with Data Mitigation for Safety Verification of Nonlinear Systems

This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing BCs often relies on an accurate dynamics model; however, such models are often imprecise due to the model complexity involved, particularly when dealing with highly nonlinear systems. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for the unknown dynamical system, they often require solving an optimization problem with substantial amounts of data. To address this, we propose a physics-informed scenario approach that selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close. This approach guides the scenario optimization process to eliminate redundant samples and potentially reduce the required dataset size. We validate our approach through three case studies, showcasing its practical application in reducing the required data.

eess.SY↗

arXiv2024

Data-Driven Control of Large-Scale Networks with Formal Guarantees: A Small-Gain Free Approach

This paper offers a data-driven divide-and-conquer strategy to analyze large-scale interconnected networks, characterized by both unknown mathematical models and interconnection topologies. Our data-driven scheme treats an unknown network as an interconnection of individual agents (a.k.a. subsystems) and aims at constructing their symbolic models, referred to as discrete-domain representations of unknown agents, by collecting data from their trajectories. The primary objective is to synthesize a control strategy that guarantees desired behaviors over an unknown network by employing local controllers, derived from symbolic models of individual agents. To achieve this, we leverage the concept of alternating sub-bisimulation function (ASBF) to capture the closeness between state trajectories of each unknown agent and its data-driven symbolic model. Under a newly developed data-driven compositional condition, we then establish an alternating bisimulation function (ABF) between an unknown network and its symbolic model, based on ASBFs of individual agents, while providing correctness guarantees. Despite the sample complexity in existing work being exponential with respect to the network size, we demonstrate that our divide-and-conquer strategy significantly reduces it to a linear scale with respect to the number of agents. We also showcase that our data-driven compositional condition does not necessitate the traditional small-gain condition, which demands precise knowledge of the interconnection topology for its fulfillment. We apply our data-driven findings to three benchmarks comprising unknown networks with an arbitrary, a-priori undefined number of agents and unknown interconnection topologies.

eess.SY↗

arXiv2024

From Data to Control: A Formal Compositional Framework for Large-Scale Interconnected Networks

We introduce a compositional data-driven methodology with noisy data for designing fully-decentralized safety controllers applicable to large-scale interconnected networks, encompassing a vast number of subsystems with unknown mathematical models. Our compositional scheme leverages the interconnection topology and breaks down the network analysis into the examination of distinct subsystems. This is accompanied by utilizing a concept of control storage certificates (CSCs) to capture joint dissipativity-type properties among subsystems. These CSCs are instrumental in a compositional derivation of a control barrier certificate (CBC) specialized for the interconnected network, thereby ensuring its safety. In our data-driven scheme, we gather only a single noise-corrupted input-state trajectory from each unknown subsystem within a specified time frame. By fulfilling a specific rank condition, this process facilitates the construction of a CSC for each subsystem. Following this, by adhering to compositional dissipativity reasoning, we compose CSCs derived from noisy data and build a CBC for the unknown network, ensuring its safety over an infinite time horizon, while providing correctness guarantees. We demonstrate that our compositional data-driven approach significantly enhances the design of a CBC and its robust safety controller under noisy data across the interconnected network. This advancement is achieved by reducing the computational complexity from a polynomial growth in relation to network dimension, when using sum-of-squares (SOS) optimization, to a linear scale based on the number of subsystems. We apply our data-driven findings to a variety of benchmarks, involving physical networks with unknown models and diverse interconnection topologies.

eess.SY↗