arXiv subjects

Matteo Tacchi-Bénard

Publications and source records attributed to Matteo Tacchi-Bénard.

6 recordsLinked to original sources

arXiv2026

Beyond Ellipsoids: Semi-Algebraic Tightening for Chance Constraints Under Actuator Saturation

Motivated by stochastic model predictive control applications, we present a semi-algebraic approach to constraint tightening for chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturated error dynamics are handled via their exact piecewise-affine structure, which naturally accommodates asymmetric saturation bounds. A polynomial Lyapunov function satisfying a drift condition is then designed using sum-of-squares optimization, yielding finite-time probabilistic reachable sets and a probabilistic ultimate bound. The set geometry is explicitly optimized for constraint tightening, further reducing conservatism. A numerical example demonstrates the effectiveness of the design.

math.OC↗

arXiv2026

Data-driven approximation of regions of attraction via an LP-based selection of PWA Lyapunov functions

This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible dynamics is constructed. This uncertainty description enables the synthesis of a continuous piece-wise affine Lyapunov candidate via a linear program, enforcing a robust decrease condition for all admissible vector fields. The approach allows certification of a region of attraction consistent with the available data. Numerical examples illustrate the effectiveness of the proposed method in extracting certified regions of attraction from sparse data.

math.OC↗

arXiv2026

The Benefits of Diversity: Combining Comparisons and Ratings for Efficient Scoring

Should humans be asked to evaluate entities individually or comparatively? This question has been the subject of long debates. In this work, we show that, interestingly, combining both forms of preference elicitation can outperform the focus on a single kind. More specifically, we introduce SCoRa (Scoring from Comparisons and Ratings), a unified probabilistic model that allows to learn from both signals. We prove that the MAP estimator of SCoRa is well-behaved. It verifies monotonicity and robustness guarantees. We then empirically show that SCoRa recovers accurate scores, even under model mismatch. Most interestingly, we identify a realistic setting where combining comparisons and ratings outperforms using either one alone, and when the accurate ordering of top entities is critical. Given the de facto availability of signals of multiple forms, SCoRa additionally offers a versatile foundation for preference learning.

cs.LG↗

arXiv2025

Optimal Control of H-Mode Tokamak Plasma Temperature based on Pontryagin's Principle

This paper studies the decay of an objective functional using a new control technique within Pontryagin's framework. Convergence analysis is carried out on the infinite-dimensional space of Tokamak plasma dynamical state as described by weakly decoupled nonlinear partial differential equations. An adjoint-based optimal control is derived to minimize the deviation from a predefined dynamical trajectory leading to the desired target state at stationary regime, by turning Pontryagin's transversality conditions into a continuum of horizons. A feedback controller is proposed to steer the system efficiently in real time, as opposed to an open-loop controller resulting from the classical Pontryagin's setting. An algorithm synthesizing the constraint-free optimal controller is used for profile tracking based on experimental data.

math.OC↗

arXiv2025

Probabilistic Reachable Set Estimation for Saturated Systems with Unbounded Additive Disturbances

In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of the saturated error dynamics that allows us to tightly bound its evolution and therefore construct accurate reachable sets. The proposed approach is applicable to independent, zero mean disturbances with a known covariance. A numerical example illustrates the applicability and effectiveness of the proposed design.

math.OC↗

arXiv2025

Sequentially learning regions of attraction from data

The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side of the ordinary differential equation governing the system is available for a set of points in the state space. Technically, a Piecewise Affine Lyapunov function will be constructed iteratively using an optimisation-based technique for the effective validation of the certificates. As a main contribution, whenever those certificates are violated locally, a refinement of the domain and the associated tessellation is produced, thus leading to an improvement in the description of the domain of attraction.

eess.SY↗