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 dimension 200.
Turnpike in optimal control and beyond: a survey
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UNVERDICTED 5representative citing papers
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 conditions.
Finite-horizon LQ N-player differential games with Gaussian data exhibit exponential turnpike convergence to ergodic equilibria uniformly in N.
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 space, with existence of stable solutions established via fixed-point methods.
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.
citing papers explorer
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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 dimension 200.
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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 conditions.
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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.
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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 space, with existence of stable solutions established via fixed-point methods.
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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.