相关论文: On damping a control system of arbitrary order wit…

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…

A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…

Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…

Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…

The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…

We study nonlinear singular optimal control problems of port-Hamil-tonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality…

We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified…

In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the…

We consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations. The focus is on boundary damping, which is implemented as a dynamic boundary condition. A change of material laws…

It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…

In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.

A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

In the present contribution we consider a singular phase field system located in a smooth and bounded three-dimensional domain. The entropy balance equation is perturbed by a logarithmic nonlinearity and by the presence of an additional…

This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…

This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…