English
Related papers

Related papers: Classical System Theory Revisited for Turnpike in …

200 papers

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

This paper investigates the long-time behavior of zero-sum stochastic linear-quadratic (SLQ) differential games within Markov regime-switching diffusion systems and establishes the turnpike property of the optimal triple. By verifying the…

Optimization and Control · Mathematics 2025-09-12 Xun Li , Fan Wu , Xin Zhang

In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the…

Optimization and Control · Mathematics 2025-10-22 Julian D. Schiller , Lars Grüne , Matthias A. Müller

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems subject to control and terminal state constraints. To this end, after reducing the problem to an ODE…

Optimization and Control · Mathematics 2022-02-16 Timm Faulwasser , Bernhard Maschke , Friedrich Philipp , Manuel Schaller , Karl Worthmann

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

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…

Optimization and Control · Mathematics 2019-07-04 Timm Faulwasser , Kathrin Flaßkamp , Sina Ober-Blöbaum , Karl Worthmann

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…

Dynamical Systems · Mathematics 2013-05-24 Augusto Ferrante , Lorenzo Ntogramatzidis

This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…

Optimization and Control · Mathematics 2025-10-21 Wenjing Yang , Zhaorong Zhang , Juanjuan Xu

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…

Optimization and Control · Mathematics 2026-02-10 Jingrui Sun , Lvning Yuan

We present a continuous-time equivalent to the well-known iterative linear-quadratic algorithm including an implementation of a backtracking line-search policy and a novel regularization approach based on the necessary conditions in the…

Systems and Control · Electrical Eng. & Systems 2025-05-22 Juraj Lieskovský , Jaroslav Bušek , Tomáš Vyhlídal

We obtain turnpike results for optimal control problems with lack of stabilizability in the state equation and/or detectability in the state term in the cost functional. We show how, under weakened stabilizability/detectability conditions,…

Optimization and Control · Mathematics 2020-07-29 Dario Pighin , Noboru Sakamoto

We study the quadratic regulator problem on a finite time horizon for the wave equation with high internal damping controlled on the boundary by square integrable controls. The approach in this paper transforms the wave equation with high…

Optimization and Control · Mathematics 2025-05-20 L. Pandolfi

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…

Analysis of PDEs · Mathematics 2020-08-11 Mahamadi Warma , Sebastian Zamorano

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e.…

Optimization and Control · Mathematics 2021-04-13 Manuel Schaller , Friedrich Philipp , Timm Faulwasser , Karl Worthmann , Bernhard Maschke

Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…

Optimization and Control · Mathematics 2025-12-19 Enrique Zuazua

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

This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control…

Optimization and Control · Mathematics 2012-09-03 Augusto Ferrante , Lorenzo Ntogramatzidis

Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of the system nonlinearities, it is shown that the optimal control problem is dissipative with…

Optimization and Control · Mathematics 2023-01-24 Attila Karsai

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…

Mathematical Finance · Quantitative Finance 2021-10-13 Hongyan Cai , Danhong Chen , Yunfei Peng , Wei Wei

One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…

Optimization and Control · Mathematics 2016-11-28 Qi Lu , Tianxiao Wang , Xu Zhang