arXiv subjects

Ali Kashani

Publications and source records attributed to Ali Kashani.

5 recordsLinked to original sources

arXiv2026

Data-Driven Personalization of Automated Insulin Delivery

Automated insulin delivery (AID) systems are often tuned for the population and offer limited online adaptation to the inter- and intrapatient variability in insulin needs caused by meal patterns, physical activity, and fluctuations in insulin sensitivity. We present a real-time, data-driven personalization approach that adapts controller parameters using the subject's daily glycemic data. The adaptation is formulated as projected gradient descent on a daily risk metric, where the gradient estimation is designed to attenuate noise and metabolic variability. We use contraction theory to validate the optimization framework and convergence of the closed-loop system under adaptation. In silico experiments on the 100-adult cohort of the FDA-accepted UVA/Padova T1D simulator show that our method improves glycemic risk and increases time-in-range (TIR, 70-180\,mg/dL) by 2%, 3%, and 4% after 4, 8, and 17 weeks, respectively, under variability in meal timing, meal size, and insulin sensitivity.

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arXiv2025

Learning Control Barrier Functions with Deterministic Safety Guarantees

Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous dynamical system is a difficult task. This work explores the design of BFs using data to obtain safe sets with deterministic assurances of control invariance. We leverage ReLU neural networks (NNs) to create continuous piecewise affine (CPA) BFs with deterministic safety guarantees for Lipschitz continuous, discrete-time dynamical system using sampled one-step trajectories. The CPA structure admits a novel classifier term to create a relaxed \ac{bf} condition and construction via a data driven constrained optimization. We use iterative convex overbounding (ICO) to solve this nonconvex optimization problem through a series of convex optimization steps. We then demonstrate our method's efficacy on two-dimensional autonomous and non-autonomous dynamical systems.

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arXiv2025

Data-driven certificates of constraint enforcement and stability for unmodeled, discrete dynamical systems using tree data structures

This paper addresses the critical challenge of developing data-driven certificates for the stability and safety of unmodeled dynamical systems by leveraging a tree data structure and an upper bound of the system's Lipschitz constant. Previously, an invariant set was synthesized by iteratively expanding an initial invariant set. In contrast, this work iteratively prunes the constraint set to synthesize an invariant set -- eliminating the need for a known, initial invariant set. Furthermore, we provide stability assurances by characterizing the asymptotic stability of the system relative to an invariant approximation of the minimal positive invariant set through synthesis of a discontinuous piecewise affine Lyapunov function over the computed invariant set. The proposed method takes inspiration from subdivision techniques and requires no prior system knowledge beyond Lipschitz continuity.

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arXiv2025

Data driven synthesis of provable invariant sets via stochastically sampled data

Positive invariant (PI) sets are essential for ensuring safety, i.e. constraint adherence, of dynamical systems. With the increasing availability of sampled data from complex (and often unmodeled) systems, it is advantageous to leverage these data sets for PI set synthesis. This paper uses data driven geometric conditions of invariance to synthesize PI sets from data. Where previous data driven, set-based approaches to PI set synthesis used deterministic sampling schemes, this work instead synthesizes PI sets from any pre-collected data sets. Beyond a data set and Lipschitz continuity, no additional information about the system is needed. A tree data structure is used to partition the space and select samples used to construct the PI set, while Lipschitz continuity is used to provide deterministic guarantees of invariance. Finally, probabilistic bounds are given on the number of samples needed for the algorithm to determine of a certain volume.

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arXiv2023

Data-driven invariant set for nonlinear systems with application to command governors

This paper presents a novel approach to synthesize positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven command governor that selects a command for the closed-loop system to enforce constraints. Using basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states and input commands. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems.

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