Related papers: Second-order Filippov systems: sliding dynamics wi…
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…
There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…
When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside…
We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows…
In the article we study a hyperbolic-elliptic system of PDE. The system can describe two different physical phenomena: 1st one is the motion of magnetic vortices in the II-type superconductor and 2nd one \ is the collective motion of cells.…
This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We…
We present new theorems characterizing robust Lyapunov functions and infinite horizon value functions in optimal control as unique viscosity solutions of partial differential equations. We use these results to further extend Zubov's method…
A two-dimensional \underline{Frenkel-Kontorova model} under a steady external force is used to study the nonlinear sliding friction between flat macroscopic surfaces with a lubricant layer in between. The nonequilibrium properties of the…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
Effective slip boundary conditions for flows over periodic micro-structured surfaces containing a secondary immiscible fluid are derived. The primary fluid is in the Cassie state, while the geometries of the micro-structures can be…
This paper concerns two algorithms for solving optimal control problems with hybrid systems. The first algorithm aims at hybrid systems exhibiting sliding modes. The first algorithm has several features which distinguishes it from the other…
We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality conditions for the optimal control of the total biomass…
We study in this paper a multilayer discretization of second order elliptic problems, aimed at providing reliable multilayer discretizations of shallow fluid flow problems with diffusive effects. This discretization is based upon the…
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…
We generalize Iskovskih's theorem about surfaces without irregularity and bigenus from the smooth case to regular surfaces over arbitrary fields, with special focus on the case of imperfect fields. This includes surfaces that are…