David Angeli

Mahdieh Zaker, David Angeli, Abolfazl Lavaei

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.

Youhong Chen, Xiaoyu Tan, Muhammad Sharjeel Javaid et al.

The growing penetration of inverter-based resources (IBRs) necessitates stability assessment methods that are scalable, decentralized, and model-agnostic. This paper develops a block diagonal dominance (BDD) criterion for decentralized small-signal stability of IBR-dominated power grids. The proposed approach forms the basis for an enhanced IBR connection compliance condition from a small-signal stability perspective that can be evaluated locally for IBRs to be connected to the grid. The proposed approach is shown to be much less conservative than strict diagonal dominance (SDD). Beyond mere stability, we ensure a minimum decay rate or maximum settling time for IBR-induced oscillation. Crucially, these are achieved without imposing restrictive assumptions on network or IBR models. The framework therefore, offers a practical and theoretically grounded basis for decentralized stability certificate of IBR-dominated power grids.

Aivar Sootla, Diego Oyarzun, David Angeli et al.

In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation.