Related papers: Turnpike property of linear quadratic control prob…
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…
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 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 devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by…
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…
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…
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
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…
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 consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…
We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential…
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…
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…
In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
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 paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and…
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained…
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…
This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper…