Related papers: The turnpike property in finite-dimensional nonlin…
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…
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control…
Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…
In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting…
In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a…
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…
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…
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…
The turnpike property refers to the phenomenon that in many optimal control problems, the solutions for different initial conditions and varying horizons approach a neighborhood of a specific steady state, then stay in this neighborhood for…
We deduce a sufficient condition of the exponential (integral) turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential…
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…
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions…
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…
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…
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…
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 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…
This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike…
An exponential turnpike property for a semilinear control problem is proved. The state-target is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also obtained for large targets, requiring that the…
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics…