Related papers: Saddle Flow Dynamics: Observable Certificates and …
This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is…
Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for…
Saddle-point models arise throughout optimization, optimal transport, robust learning, and control. In many applications, the relevant function f(x,y) is convex in x and concave in y, and preserving this geometry is essential for obtaining…
This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…
We consider the problem of convergence to a saddle point of a concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz and Uzawa in [1] such dynamics have been extensively used in diverse areas, there are,…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal…
In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of…
The authors in (Banjac et al., 2019) recently showed that the Douglas-Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
This paper addresses the critical challenge of developing data-driven certificates for the stability and safety of unmodeled dynamical systems by leveraging a tree data structure and an upper bound of the system's Lipschitz constant.…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
Many systems contain latent variables that make their dynamics partially unidentifiable or cause distribution shifts in the observed statistics between offline and online data. However, existing control techniques often assume access to…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…