Related papers: Turnpike Properties in Optimal Control: An Overvie…
This paper investigates the relations between three different properties, which are of importance in optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady…
The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide class of long-horizon optimal control problems, the optimal trajectory spends most of its time near a steady-state solution (the…
We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the…
The \emph{turnpike property} in contemporary macroeconomics asserts that if an economic planner seeks to move an economy from one level of capital to another, then the most efficient path, as long as the planner has enough time, is to…
We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key…
This paper considers an optimal control problem for a linear mean-field stochastic differential equation having regime switching with quadratic functional in the large time horizons. Our main contribution lies in establishing the strong…
We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the…
Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal…
We investigate the interior turnpike phenomenon for discrete-time multi-agent optimal control problems. While for continuous systems the turnpike property has been established, we focus here on first-order discretizations of such systems.…
This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time horizon $[0,T]$ as $T\rightarrow\infty$. The so-called turnpike properties are established for such problems, under…
This work is concerned with a hierarchical framework of optimal control problems connecting interacting particle systems, the mean field limit equations, and associated hydrodynamic models. By assuming the existence of solutions, we…
This paper is concerned with an optimal control problem for a mean-field linear stochastic differential equation with a quadratic functional in the infinite time horizon. Under suitable conditions, including the stabilizability, the…
This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…
Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control…
In this paper the turnpike property is established for a non-convex optimal control problem in discrete time. The functional is defined by the notion of the ideal convergence and can be considered as an analogue of the terminal functional…
This paper is devoted to the study of the turnpike phenomenon arising in the optimal distributed control tracking-type problem for the Navier-Stokes equations. We obtain a positive answer to this property in the case when the controls are…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…
In this paper, we develop several necessary conditions of turnpike property for generalizaid linear-quadratic (LQ) optimal control problem in infinite dimensional setting. The term 'generalized' here means that both quadratic and linear…
This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate…
The paper proposes first steps towards the formalization and characterization of time-varying turnpikes in optimal control of mechanical systems. We propose the concepts of velocity steady states, which can be considered as partial steady…