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A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Saleh Mobayen, Fairouz Tchier (2015)

Kybernetika

This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...

A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.

A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.

Adjoint methods for obstacle problems and weakly coupled systems of PDE

Filippo Cagnetti, Diogo Gomes, Hung Vinh Tran (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.

Catastrophes and partial differential equations

John Guckenheimer (1973)

Annales de l'institut Fourier

This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity are discussed....

Connecting orbits of time dependent Lagrangian systems

Patrick Bernard (2002)

Annales de l’institut Fourier

We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.

Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain

Masatake Miyake, Akira Shirai (2000)

Annales Polonici Mathematici

We study the convergence or divergence of formal (power series) solutions of first order nonlinear partial differential equations    (SE) f(x,u,Dx u) = 0 with u(0)=0. Here the function f(x,u,ξ) is defined and holomorphic in a neighbourhood of a point ( 0 , 0 , ξ 0 ) x n × u × ξ n ( ξ 0 = D x u ( 0 ) ) and f ( 0 , 0 , ξ 0 ) = 0 . The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0 ( ξ n ) . The criterion of convergence of a formal solution u ( x ) = | α | 1 u α x α of (SE) is given by a generalized form of the Poincaré condition which depends on each formal solution. In the case where the formal...

Convergenza per l'equazione degli integrali primi associata al problema del rimbalzo

Michele Carriero, Antonio Leaci, Eduardo Pascali (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).

Diffusion limit of the Lorentz model : asymptotic preserving schemes

Christophe Buet, Stéphane Cordier, Brigitte Lucquin-Desreux, Simona Mancini (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...

Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes

Christophe Buet, Stéphane Cordier, Brigitte Lucquin-Desreux, Simona Mancini (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...

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