# Global stabilization in nonlinear discrete systems with time-delay

@article{Ivanov2013GlobalSI, title={Global stabilization in nonlinear discrete systems with time-delay}, author={Anatoli F. Ivanov and Musa A. Mammadov and Sergei I. Trofimchuk}, journal={Journal of Global Optimization}, year={2013}, volume={56}, pages={251-263} }

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.

## 6 Citations

Turnpike Theorem for an Infinite Horizon Optimal Control Problem with Time Delay

- MathematicsSIAM J. Control. Optim.
- 2014

The existence of optimal solutions as well as the asymptotic stability of optimal trajectories are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem.

Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations

- MathematicsJournal of biological dynamics
- 2017

This work analyses the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals, and implements a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.

On convergence of solutions to difference equations with additive perturbations

- Mathematics
- 2016

Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive…

SINGULAR PERTURBATIONS AND TIME SCALES IN CONTROL THEORIES AND APPLICATIONS: AN OVERVIEW 2002-2012

- Environmental Science
- 2011

This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 2002-2012. The previous overviews/surveys were provided for the…

Robust optimization for a nonlinear switched time-delay system with noisy output measurements using hybrid optimization algorithm

- Engineering, MathematicsJ. Frankl. Inst.
- 2019

TURNPIKE THEOREMS FOR CONVEX PROBLEMS WITH UNDISCOUNTED INTEGRAL FUNCTIONALS

- Economics, Mathematics
- 2013

In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having…

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