arXiv subjects

Sixiong You

Publications and source records attributed to Sixiong You.

4 recordsLinked to original sources

arXiv2026

An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control

Heterogeneous mean-field control (MFC) involves multiple interacting populations with distinct dynamics, control constraints, and coupling structures. We develop a heterogeneous occupation-measure mean-field control (OM-MFC) framework that reformulates the population-distribution control problem as an optimization problem over occupation measures. In this representation, potentially nonlinear dynamics enter through linear weak Liouville constraints, while nonlocal inter-population interactions become structured bilinear functionals of the occupation-measure marginals. Exploiting this structure, we derive a Frank--Wolfe (FW) method and show that its linear minimization oracle decomposes into independent population-wise optimal control problems once the current population distributions are fixed, enabling parallel computation without an a priori discretization of the measure space. We further establish a sufficient convexity condition based on the symmetrized matrix-valued interaction kernel, under which Frank--Wolfe with an exact oracle admits the standard $O(1/k)$ convergence rate. Numerical examples on heterogeneous UAV coordination and three-dimensional search-and-rescue illustrate the framework both within the certified convex regime and for directional interactions beyond that regime.

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arXiv2026

Convexifying Mean-Field Control: An Occupation-Measure and Frank-Wolfe Approach

Large-scale robotic swarms motivate the use of mean-field control (MFC). Classical partial differential equation (PDE)-based formulations provide a principled framework but can become computationally challenging in higher dimensions, whereas machine learning achieves scalability at the cost of approximation and guarantees. In this work, we establish an optimization-based framework that lifts the MFC problem into the space of occupation measures, resulting in a convex relaxation formulated as an optimization over measures. The resulting problem is solved using a Frank-Wolfe (FW) algorithm in the measure space, with each iteration reduced to a tractable optimal control problem. This approach retains the O(1/k) convergence rate of FW, avoids discretization of the state space, and naturally incorporates interaction and safety constraints. Numerical experiments demonstrate agreement with analytic and PDE-based baselines in two dimensions and show that the method scales to three-dimensional environments with multiple obstacles, where standard grid-based PDE solvers become impractical. A full 3D instance with ten obstacles is solved in minutes on a standard workstation, underscoring the practicality and scalability of the proposed framework.

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arXiv2026

Occupation-Measure Mean-Field Control: Optimization over Measures and Frank-Wolfe Methods

Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework for large-population control, termed occupation-measure mean-field control (OM-MFC). The framework models the evolution of agent populations directly in the space of occupation measures and casts large-population control as an infinite-dimensional optimization problem over measures, which becomes convex under a positive-semidefiniteness condition on the interaction kernel. A Frank--Wolfe (FW) algorithm and its fully-corrective variant (FCFW) are developed to solve the resulting problem efficiently, where each iteration reduces to a classical optimal control subproblem. Theoretical results establish convexity, existence of optimal solutions, and convergence guarantees of the proposed algorithms. Owing to its measure-based formulation, the framework naturally accommodates systems with very large numbers of agents. Numerical experiments on UAV swarm coordination and satellite constellation control demonstrate the scalability and effectiveness of the proposed approach in high-dimensional and constrained environments.

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arXiv2019

Learning-based Hamilton-Jacobi-Bellman Methods for Optimal Control

Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the difficulty of guessing the adjoint variables. This paper proposes two learning-based approaches to find the initial guess of adjoint variables in real-time, which can be applied to solve general TPBVPs. For cases with database of solutions and corresponding adjoint variables of a TPBVP under varying boundary conditions, a supervised learning method is applied to learn the HJB solutions off-line. After obtaining a trained neural network from supervised learning, we are able to find proper initial adjoint variables for given boundary conditions in real-time. However, when validated solutions of TPBVPs are not available, the reinforcement learning method is applied to solve HJB by constructing a neural network, defining a reward function, and setting appropriate super parameters. The reinforcement learning based HJB method can learn how to find accurate adjoint variables via an updating neural network. Finally, both learning approaches are implemented in classical optimal control problems to verify the effectiveness of the learning based HJB methods.

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