English
Related papers

Related papers: A flatness proof of the exponential turnpike pheno…

200 papers

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…

Optimization and Control · Mathematics 2025-03-13 Fabio Cassini , Chiara Segala

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…

Optimization and Control · Mathematics 2025-10-24 Erhan Bayraktar , Jiamin Jian

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…

Analysis of PDEs · Mathematics 2018-11-08 Martin Gugat , Falk Hante

This paper presents a simulation study on turnpike phenomena in stochastic optimal control problems. We employ the framework of Polynomial Chaos Expansions (PCE) to investigate the presence of turnpikes in stochastic LQ problems. Our…

Systems and Control · Electrical Eng. & Systems 2020-10-26 Ruchuan Ou , Michael Heinrich Baumann , Lars Grüne , Timm Faulwasser

We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our…

Optimization and Control · Mathematics 2026-03-03 Alexander Zuyev , Emmanuel Trélat

Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the…

Optimization and Control · Mathematics 2024-10-10 Cédric Join , Emmanuel Delaleau , Michel Fliess

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

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…

Analysis of PDEs · Mathematics 2021-11-23 Carlos Esteve , Hicham Kouhkouh , Dario Pighin , Enrique Zuazua

We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end,…

Optimization and Control · Mathematics 2022-03-02 Lars Grüne , Manuel Schaller , Anton Schiela

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with…

Optimization and Control · Mathematics 2022-02-18 Lars Grüne , Lisa Krügel

The classical Euler's problem on stationary configurations of elastic rod with fixed endpoints and tangents at the endpoints is considered as a left-invariant optimal control problem on the group of motions of a two-dimensional plane…

Optimization and Control · Mathematics 2007-05-23 Yu. L. Sachkov

We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T , by minimizing an objective…

Optimization and Control · Mathematics 2015-05-20 Martin Gugat , Emmanuel Trélat , Enrique Zuazua

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…

Optimization and Control · Mathematics 2021-03-17 Timm Faulwasser , Lars Grüne

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…

Optimization and Control · Mathematics 2020-05-26 Timm Faulwasser , Lars Grüne , Jukka-Pekka Humaloja , Manuel Schaller

This paper presents analyses for the maximum hands-off control using the geometric methods developed for the theory of turnpike in optimal control. First, a sufficient condition is proved for the existence of the maximum hands-off control…

Optimization and Control · Mathematics 2020-05-01 Noboru Sakamoto , Masaaki Nagahara

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…

Optimization and Control · Mathematics 2021-08-24 Zhong-Jie Han , Enrique Zuazua

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…

Systems and Control · Computer Science 2017-07-18 Timm Faulwasser , Milan Korda , Colin N. Jones , Dominique Bonvin

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…

Optimization and Control · Mathematics 2022-11-01 Musa Mammadov , Piotr Szuca

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…

Optimization and Control · Mathematics 2017-05-09 Emmanuel Trelat , Can Zhang

We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…

Optimization and Control · Mathematics 2024-08-01 Daniel Wachsmuth