Publications

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Manuscripts and Preprints

Towards Bridging Data-Driven Control Synthesis with Hamiltonian-Jacobi-Bellman Theory

Published in MAE 546 Term Paper, 2025

Synthesising robust control policies for uncertain dynamical systems is traditionally hindered by the computational intractability of the Hamilton-Jacobi-Bellman equation, particularly in high-dimensional or parametric settings. To address this, we propose a data-driven framework that bridges classical optimal control theory with certificate synthesis. Leveraging the Scenario Approach, we extend the subsurface descent algorithm to jointly learn a robust controller and a corresponding reachability certificate from a finite set of sampled parameters. We demonstrate that the certificate conditions function as a relaxation of the discrete-time Bellman equation, with the certificate approximating the optimal Value Function. Numerical validation confirms that the synthesised data-driven controller closely approximates the optimal policy, offering a scalable alternative for robust control synthesis without requiring explicit solutions to partial differential equations.

Recommended citation: Claudio Vestini. (2025). "Towards Bridging Data-Driven Control Synthesis with Hamiltonian-Jacobi-Bellman Theory." MAE 546 Term Paper.
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Fast-Forwarding Stalling in Dykstra’s Algorithm

Published in arXiv preprint arXiv:2511.18132, 2025

Constrained quadratic programs and Euclidean projections are ubiquitous in engineering, arising in machine learning, estimation, control, and signal processing. Dykstra’s algorithm is an iterative scheme for computing the Euclidean projection of an initial point onto the intersection of convex sets by successively projecting onto each set. Its low per-iteration computational cost makes it well-suited for solving large-scale or real-time problems where traditional optimisation routines become computationally burdensome. Despite its strong convergence guarantees, Dykstra’s algorithm is known to suffer from stalling – arbitrarily long intervals during which the primal iterates remain constant – rendering its runtime unpredictable and severely limiting its applicability in time-critical settings. Focusing on polyhedral constraint sets, we derive a closed-form solution for the length of the stalling period once stalling is detected. This result enables a modified, stall-averse version of Dykstra’s algorithm that fast-forwards the stalling period via a single, inexpensive update while preserving convergence guarantees. Numerical experiments demonstrate substantial improvements in convergence behaviour, establishing the proposed method as a practical enhancement for a broad class of projection-based algorithms.

Recommended citation: Claudio Vestini, Idris Kempf. (2025). "Fast-Forwarding Stalling in Dykstra's Algorithm." arXiv preprint arXiv:2511.18132.
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Oxford Third-Year Project (3YP)

Materials Testing for Heatshield Applications during CubeSat Re-entry with Passive Demise

Published in Department of Engineering Science, University of Oxford, 2025

The development of reliable heat shield materials for commercial re-entry vehicles requires experimental validation under real-world hypersonic conditions, a challenge that traditional ground-based testing cannot adequately address. This report presents the innovative design of an 8U CubeSat intended to serve as an experimental testing platform for heatshield materials in commercial applications. The satellite deploys from a RocketLab Electron launch vehicle at 400 km altitude and performs semi-controlled re-entry using cold gas thrusters and a reaction wheel system. Beginning at an altitude of 150 km, integrated thermocouples, pressure transducers, recession sensors, and a spectrometer capture material performance and atmospheric impact data, while a novel phased array bidirectional communication system indirectly transmits through the CubeSat’s wake to a ground station via the Iridium network. Comprehensive numerical modelling validates mission feasibility and predicts thermal and aerodynamic loading throughout re-entry phases. At an estimated cost of £700,000, each mission provides the customer with otherwise inaccessible experimental data on material behaviour under extreme hypersonic conditions, directly addressing the current scarcity of validated re-entry design data and advancing design-for-demise methodologies.

Recommended citation: Claudio Vestini, F. Naqvi, H. Moussa, A. Berresford. (2025). "Materials Testing for Heatshield Applications during CubeSat Re-entry with Passive Demise." Third-Year Project (3YP).
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