Related papers: Local Nash Realizations
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…
This paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regards to the optimization of a common objective function. In the resulting zero-sum game, individual agents collaborate with…
In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. It is…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
Data similarity (or distance) computation is a fundamental research topic which fosters a variety of similarity-based machine learning and data mining applications. In big data analytics, it is impractical to compute the exact similarity of…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of…
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
In this paper we study social exclusion in social (information) networks using a game-theoretic approach, and study the stability of a certain class community structures that are a Nash equilibrium. The main result of our analysis shows…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
We report a practical finite-time algorithmic scheme to compute approximately stationary points for nonconvex nonsmooth Lipschitz functions. In particular, we are interested in two kinds of approximate stationarity notions for nonconvex…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
We address Nash problem for surface singularities using wedges. We give a refinement of the characterisation of A. Reguera of the image of the Nash map in terms of wedges. Our improvement consists in a characterisation of the bijectivity of…