相关论文: Classical System Theory Revisited for Turnpike in …

We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…

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…

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…

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…

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 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…

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…

Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the…

We investigate convergence and turnpike properties for linear-quadratic mean field control problems with common noise. Within a unified framework, we analyze a finite-horizon social optimization problem, its mean field control limit, and…

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity…

We revisit finite-dimensional linear-quadratic optimal control from the viewpoint of differential flatness. If the pair (A, B) is controllable, then the linear control system is flat, and every trajectory can be parametrized by a flat…

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…

We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…

In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike effect persists in the presence of noise…

In this paper we investigate the turnpike property for constrained LQ optimal control problem in connection with dissipativity of the control system. We determine sufficient conditions to ensure the turnpike property in the case of a…

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 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…

We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By comparing the finite-horizon game with its ergodic counterpart, we establish…

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…

We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…