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Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
General distribution steering is intrinsically an infinite-dimensional problem, when the continuous distributions to steer are arbitrary. We put forward a moment representation of the primal system for control in [42]. However, the system…
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…
Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
The notion of strong structural controllability (s-controllability) allows for determining controllability properties of large linear time-invariant systems even when numerical values of the system parameters are not known a priori. The…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Given a graph G=(V, E), a vertex is said to ve-dominate an edge if it is either incident with the edge or adjacent to one of its endpoints. A set of vertices is a ve-dominating set if it ve-dominates every edge of the graph. We introduce…
Let $G$ be a semidirect product of a simply connected nilpotent Lie group and $\R$. For a left invariant control system on $G$ with a convex cone as a control domain, it is proved that the attainable sets coincides with a "halfspace" if the…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
Discrete-time stochastic optimal control remains a challenging problem for general, nonlinear systems under significant uncertainty, with practical solvers typically relying on the certainty equivalence assumption, replanning and/or…
The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts'…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…
We consider the problem of controller synthesis under imperfect information in a setting where there is a set of available observable predicates equipped with a cost function. The problem that we address is the computation of a subset of…
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
Model Predictive Control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some…