Amy Nejati

MohammadHossein Ashoori, Ali Aminzadeh, Amy Nejati et al.

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.

Mahdieh Zaker, Amy Nejati, Abolfazl Lavaei

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.

Mahdieh Zaker, Andrii Mironchenko, Amy Nejati et al.

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.

Ali Aminzadeh, MohammadHossein Ashoori, Amy Nejati et al.

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.