We provide a framework for robust mean field control problems that describe multi-dimensional optimal liquidation problems under uncertainty from both the underlying stochastic process and the deterministic model parameters. The verification results are established with Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations where the variables are probability measures and the Hamiltonian nonlinearly involves the joint distribution of position and momentum. Using novel a priori estimates, we establish the well-posedness of the HJBI equations featuring general or quadratic Hamiltonians that are neither displacement convex nor concave in their momentum. The a priori estimates and well-posedness results are extended during their application to optimal liquidation problems, where we allow the Hamiltonian to have derivatives of linear growth and solve the constrained multi-dimensional linear quadratic optimal liquidation problem under composite uncertainty.
Generalized semi-infinite programs (GSIPs) arise in robust optimal control whenever the admissible uncertainty depends on the state or controls. Existing GSIP methods either impose restrictive structural assumptions or require global optimization that scales poorly to control problems. We present a general framework th...
Jad Wehbeh, E. Kerrigan, Edoardo Scaccia· 0 citations
This article introduces a numerical optimal control framework for minmax constrained density control for a class of noisy linear parabolic partial differential equations (PDEs), in particular the noisy heat equation. The goal is to transport an initial density to a target density while minimizing a specified cost with...
Siddhartha Ganguly, Vaibhav Upadhyay, Kenji Kashima et al.· 0 citations
It is shown that the state distribution of the system can be tractably approximated over time by Gaussian mixture distributions, with formal error bounds in Wasserstein distance, which yields closed-form expressions for expected costs and chance constraints.
Konstantinos Prattis, Luca Laurenti, A. Dabiri· 0 citations
This paper develops a convex tube model predictive control formulation for constrained nonlinear systems. We consider dynamics described by a discrete-time state-space model with parametric and additive uncertainty that admits a difference-of-convex decomposition. Convex directional bounds of the nonlinear dynamics are...
Filippo Badalamenti, J. A. Borja-Conde, Filiberto Fele et al.· 0 citations
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochas...
Eloıse Berthier, Z. Kobeissi, F. Bach· 0 citations
We investigate a robust mean-field linear-quadratic (MFLQ) control problem under partial observation. Two candidate models are evaluated through a worst-case criterion, while the state dynamics contain mean-field terms and the observation. We derive a sufficient optimality condition, a filtered state feedback represent...
Qiang-Jun Tang· Mathematics· 0 citations
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