arXiv subjects

Abolfazl Lavaei

Publications and source records attributed to Abolfazl Lavaei.

At least 37 records · Page 2Linked to original sources

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.

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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.

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arXiv2025

From Dissipativity Property to Data-Driven GAS Certificate of Degree-One Homogeneous Networks with Unknown Topology

In this work, we propose a data-driven divide and conquer strategy for the stability analysis of interconnected homogeneous nonlinear networks of degree one with unknown models and a fully unknown topology. The proposed scheme leverages joint dissipativity-type properties of subsystems described by storage functions, while providing a stability certificate over unknown interconnected networks. In our data-driven framework, we begin by formulating the required conditions for constructing storage functions as a robust convex program (RCP). Given that unknown models of subsystems are integrated into one of the constraints of the RCP, we collect data from trajectories of each unknown subsystem and provide a scenario convex program (SCP) that aligns with the original RCP. We solve the SCP as a linear program and construct a storage function for each subsystem with unknown dynamics. Under some newly developed data-driven compositionality conditions, we then construct a Lyapunov function for the fully unknown interconnected network utilizing storage functions derived from data of individual subsystems. We show that our data-driven {divide and conquer strategy} provides correctness guarantees (as opposed to probabilistic confidence) while significantly mitigating the sample complexity problem existing in data-driven approaches. To illustrate the effectiveness of our proposed results, we apply our approaches to three different case studies involving interconnected homogeneous (nonlinear) networks with unknown models. We collect data from trajectories of unknown subsystems and verify the global asymptotic stability (GAS) of the interconnected system with a guaranteed confidence.

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arXiv2025

Safety Controller Synthesis for Stochastic Networked Systems under Communication Constraints

This paper develops a framework for synthesizing safety controllers for discrete-time stochastic linear control systems (dt-SLS) operating under communication imperfections. The control unit is remote and communicates with the sensor and actuator through an imperfect wireless network. We consider a constant delay in the sensor-to-controller channel (uplink), and data loss in both sensor-to-controller and controller-to-actuator (downlink) channels. In our proposed scheme, data loss in each channel is modeled as an independent Bernoulli-distributed random process. To systematically handle the uplink delay, we first introduce an augmented discrete-time stochastic linear system (dt-ASLS) by concatenating all states and control inputs that sufficiently represent the state-input evolution of the original dt-SLS under the delay and packet loss constraints. We then leverage control barrier certificates for dt-ASLS to synthesize a controller that ensures the stochastic safety of dt-SLS, guaranteeing that all trajectories remain outside unsafe regions with a quantified probabilistic bound. Our approach translates safety constraints into matrix inequalities, leading to an optimization problem that eventually quantifies the probability of satisfying the safety specification in the presence of communication imperfections. We validate our results on an RLC circuit subject to both constant delay and probabilistic data loss.

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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

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.

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arXiv2025

Learning Robust Safety Controllers for Uncertain Input-Affine Polynomial Systems

This paper offers a direct data-driven approach for learning robust control barrier certificates (R-CBCs) and robust safety controllers (R-SCs) for discrete-time input-affine polynomial systems with unknown dynamics under unknown-but-bounded disturbances. The proposed method relies on data from input-state observations collected over a finite-time horizon while satisfying a specific rank condition to ensure the system is persistently excited. Our data-driven scheme enables the synthesis of R-CBCs and R-SCs directly from observed data, bypassing the need for explicit modeling of the system's dynamics and thus ensuring robust system safety against disturbances within an infinite time horizon. Our proposed approach is formulated as a sum-of-squares (SOS) optimization problem, providing a structured design framework. Two case studies showcase our method's capability to provide robust safety guarantees for unknown input-affine polynomial systems under bounded disturbances, demonstrating its practical effectiveness.

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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 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.

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arXiv2025

PRoTECT: Parallelized Construction of Safety Barrier Certificates for Nonlinear Polynomial Systems

We develop an open-source software tool, called PRoTECT, for the parallelized construction of safety barrier certificates (BCs) for nonlinear polynomial systems. This tool employs sum-of-squares (SOS) optimization programs to systematically search for polynomial-type BCs, while aiming to verify safety properties over four classes of dynamical systems: (i) discrete-time stochastic systems, (ii) discrete-time deterministic systems, (iii) continuous-time stochastic systems, and (iv) continuous-time deterministic systems. PRoTECT is implemented in Python as an application programming interface (API), offering users the flexibility to interact either through its user-friendly graphic user interface (GUI) or via function calls from other Python programs. PRoTECT leverages parallelism across different barrier degrees to efficiently search for a feasible BC.

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arXiv2025

Data-Driven Dynamic Controller Synthesis for Discrete-Time General Nonlinear Systems

Synthesizing safety controllers for general nonlinear systems is a highly challenging task, particularly when the system models are unknown, and input constraints are present. While some recent efforts have explored data-driven safety controller design for nonlinear systems, these approaches are primarily limited to specific classes of nonlinear dynamics (e.g., polynomials) and are not applicable to general nonlinear systems. This paper develops a direct data-driven approach for discrete-time general nonlinear systems, facilitating the simultaneous learning of control barrier certificates (CBCs) and dynamic controllers to ensure safety properties under input constraints. Specifically, by leveraging the adding-one-integrator approach, we incorporate the controller's dynamics into the system dynamics to synthesize a virtual static-feedback controller for the augmented system, resulting in a dynamic safety controller for the actual dynamics. We collect input-state data from the augmented system during a finite-time experiment, referred to as a single trajectory. Using this data, we learn augmented CBCs and the corresponding virtual safety controllers, ensuring the safety of the actual system and adherence to input constraints over a finite time horizon. We demonstrate that our proposed conditions boil down to some data-dependent linear matrix inequalities (LMIs), which are easy to satisfy. We showcase the effectiveness of our data-driven approach through two case studies: one exhibiting significant nonlinearity and the other featuring high dimensionality.

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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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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.

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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.

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arXiv2024

Learning k-Inductive Control Barrier Certificates for Unknown Nonlinear Dynamics Beyond Polynomials

This work is concerned with synthesizing safety controllers for discrete-time nonlinear systems beyond polynomials with unknown mathematical models using the notion of k-inductive control barrier certificates (k-CBCs). Conventional CBC conditions (with k=1) for ensuring safety over dynamical systems are often restrictive, as they require the CBCs to be non-increasing at every time step. Inspired by the success of k-induction in software verification, k-CBCs relax this requirement by allowing the barrier function to be non-increasing over k steps, while permitting k-1 (one-step) increases, each up to a threshold epsilon. This relaxation enhances the likelihood of finding feasible k-CBCs while providing safety guarantees across the dynamical systems. Despite showing promise, existing approaches for constructing k-CBCs often rely on precise mathematical knowledge of system dynamics, which is frequently unavailable in practical scenarios. In this work, we address the case where the underlying dynamics are unknown, a common occurrence in real-world applications, and employ the concept of persistency of excitation, grounded in Willems et al.'s fundamental lemma. This result implies that input-output data from a single trajectory can capture the behavior of an unknown system, provided the collected data fulfills a specific rank condition. We employ sum-of-squares (SOS) programming to synthesize the k-CBC as well as the safety controller directly from data while ensuring the safe behavior of the unknown system. The efficacy of our approach is demonstrated through a set of physical benchmarks with unknown dynamics, including a DC motor, an RLC circuit, a nonlinear nonpolynomial car, and a nonlinear polynomial Lorenz attractor.

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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

Towards Mitigating Sim2Real Gaps: A Formal Quantitative Approach

In this paper, we introduce the notion of simulation-gap functions to formally quantify the potential gap between an approximate nominal mathematical model and the high-fidelity simulator representation of a real system. Given a nominal mathematical model alongside a quantified simulation gap, the system can be conceptualized as one characterized by bounded states and input-dependent disturbances. This allows us to leverage the existing powerful model-based control algorithms effectively, ensuring the enforcement of desired specifications while guaranteeing a seamless transition from simulation to real-world application. To provide a formal guarantee for quantifying the simulation gap, we develop a data-driven approach. In particular, we collect data using high-fidelity simulators, leveraging recent advancements in Real-to-Sim transfer to ensure close alignment with reality. We demonstrate the effectiveness of the proposed method through experiments conducted on a nonlinear pendulum system and a nonlinear Turtlebot model in simulators.

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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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