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Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of...
We consider a class of multiuser optimization problems in which user interactions are seen through congestion cost functions or coupling constraints. Our primary emphasis lies on the convergence and error analysis of distributed algorithms in which users communicate through aggregate user information. Traditional implementations are reliant on strong convexity assumptions, require coordination across...
We consider generalized noncooperative Nash games with ??shared constraints?? in which there is a common constraint that players' strategies are required to satisfy. We address two shortcomings that the associated generalized Nash equilibrium (GNE) is known to have: (a) shared constraint games usually have a large number (often a manifold) of GNEs and (b) the GNE may not be the appropriate solution...
Thalamus is concerned with the relay of visual information from the retina to the visual cortex. Interestingly, the information transfer is strongly mediated by nonlinear dynamics of the neurons. In particular, experiments have shown that the thalamic neurons process visual input in two distinct nonlinear dynamic modes, the so-called tonic mode and the burst mode. This paper is concerned with a bifurcation...
This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is...
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