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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Mouffak Benchohra, Lech Górniewicz, Sotiris K. Ntouyas (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.

Controllability theorem for nonlinear dynamical systems

Michał Kisielewicz (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.

Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m -input, m -output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals r by the output y of any system in 𝒮 : given λ ≥ 0 , construct a feedback strategy which ensures that, for every r (assumed bounded...

Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2008)

ESAIM: Control, Optimisation and Calculus of Variations

A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m-input, m-output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals r by the output y of any system in 𝒮 : given λ ≥ 0 , construct a feedback strategy which ensures that, for every r (assumed bounded with...

Convergence acceleration of shifted L R transformations for totally nonnegative Hessenberg matrices

Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura (2020)

Applications of Mathematics

We design shifted L R transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted L R transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted L R transformations by considering the concept of the Newton shift....

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2001)

ESAIM: Control, Optimisation and Calculus of Variations

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

Convergence estimate for second order Cauchy problems with a small parameter

Branko Najman (1998)

Czechoslovak Mathematical Journal

We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter ε . The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.

Currently displaying 301 – 320 of 394