Samuel Martin

Antoine Girard, Samuel Martin

In this paper, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart.

Rebecca Scholefield, Samuel Martin, Otto Barten

The malicious use or malfunction of advanced general-purpose AI (GPAI) poses risks that, according to leading experts, could lead to the 'marginalisation or extinction of humanity.' To address these risks, there are an increasing number of proposals for international agreements on AI safety. In this paper, we review recent (2023-) proposals, identifying areas of consensus and disagreement, and drawing on related literature to assess their feasibility. We focus our discussion on risk thresholds, regulations, types of international agreement and five related processes: building scientific consensus, standardisation, auditing, verification and incentivisation. Based on this review, we propose a treaty establishing a compute threshold above which development requires rigorous oversight. This treaty would mandate complementary audits of models, information security and governance practices, overseen by an international network of AI Safety Institutes (AISIs) with authority to pause development if risks are unacceptable. Our approach combines immediately implementable measures with a flexible structure that can adapt to ongoing research.

Samuel Martin, Irinel-Constantin Morarescu, Dragan Nesic

The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to densely and intensively connected clusters into aggregate variables. It will be shown that under suitable conditions, the states of the agents in each cluster converge fast toward a local agreement. Local agreements correspond to aggregate variables which slowly converge to consensus. Existing results concerning the time-scale separation in large networks focus on fixed and undirected graphs. The aim of this work is to extend these results to the more general case of time-varying directed topologies. It is noteworthy that in the fixed and undirected graph case the average of the states in each cluster is time-invariant when neglecting the interactions between clusters. Therefore, they are good candidates for the aggregate variables. This is no longer possible here. Instead, we find suitable time-varying weights to compute the aggregate variables as time-invariant weighted averages of the states in each cluster. This allows to deal with the more challenging time-varying directed graph case. We end up with a singularly perturbed system which is analyzed by using the tools of two time-scales averaging which seem appropriate to this system.

Samuel Martin, Julien M. Hendrickx

We consider continuous-time consensus systems whose interactions satisfy a form or reciprocity that is not instantaneous, but happens over time. We show that these systems have certain desirable properties: They always converge independently of the specific interactions taking place and there exist simple conditions on the interactions for two agents to converge to the same value. This was until now only known for systems with instantaneous reciprocity. These result are of particular relevance when analyzing systems where interactions are a priori unknown, being for example endogenously determined or random. We apply our results to an instance of such systems.