Turnpike in optimal control and beyond: a survey
read the original abstract
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 ''turnpike'') rather than being influenced by the initial or final conditions. In this article, we provide a survey on the turnpike property in optimal control, adding several recent and novel considerations. After some historical insights, we present an elementary proof of the exponential turnpike property for linear-quadratic optimal control problems in finite dimension. Next, we show an extension to nonlinear optimal control problems, with a local exponential turnpike property. On simple but meaningful examples, we illustrate the local and global aspects of the turnpike theory, clarifying the global picture and raising new questions. We discuss key generalizations, in infinite dimension and other various settings, and review several applications of the turnpike theory across different fields.
This paper has not been read by Pith yet.
Forward citations
Cited by 5 Pith papers
-
Tropical low-rank approximation and application to optimal control of N-body systems
A trajectory-based tropical low-rank approximation generates monotone lower bounds for value functions in N-body optimal control that converge to the exact value at the initial state and optimal trajectory, scaling to...
-
A flatness proof of the exponential turnpike phenomenon for linear-quadratic optimal control problems
Differential flatness reduces the Euler-Lagrange equation of controllable LQ problems to exponential-polynomial solutions whose stable-unstable splitting produces the exponential turnpike under stated nondegeneracy co...
-
Turnpike properties in linear quadratic Gaussian N-player differential games
Finite-horizon LQ N-player differential games with Gaussian data exhibit exponential turnpike convergence to ergodic equilibria uniformly in N.
-
The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian
Under a local second-order strict positivity condition on stationary equilibria, mean field game systems with quadratic Hamiltonians exhibit an exponential turnpike property near those equilibria on tori and Euclidean...
-
Ensemble optimal control for managing drug resistance in cancer therapies
Ensemble optimal control on a competitive cell population model yields an 'Off-On' adaptive therapy strategy for prostate cancer that mimics active surveillance in simulations.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.