Related papers: Stability and Optimization in Structured Populatio…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
The main result relates to structured robust stability analysis of an input-output model for networks with link uncertainty. It constitutes a collection of integral quadratic constraints, which together imply robust stability of the…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
In this paper we propose an existence and uniqueness theory for the solutions of a system of non-linear hyperbolic conservation laws, structured in age and maturity variables, representing a tissue environment. In particular we are…
We establish a general framework that guarantees the preservation of optimal control patterns as the time horizon $[0,T]$ increases and becomes unbounded. A concept of pattern-preserving family of optimal control problems is introduced and…
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the…
We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover,…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects…