Related papers: Generalized optimal transport and mean field contr…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which…
Distributed control problems under some specific information constraints can be formulated as (possibly infinite dimensional) convex optimization problems. The underlying motivation of this work is to develop an understanding of the optimal…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
Transferring the state of a quantum system to a given distribution of populations is an important problem with applications to Quantum Chemistry and Atomic Physics. In this work we consider exact population transfers that minimize the L^2…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
In this paper, we aim to explore optimal regional trajectory tracking control problems of the anomalous subdiffusion processes governed by time-fractional diffusion systems under the Neumann boundary conditions. Using eigenvalue theory of…
We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…
In this paper, a distributed optimal steady-state regulation problem is formulated and investigated for heterogeneous linear multi-agent systems subject to external disturbances. We aim to steer this high-order multi-agent network to a…
In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this…
This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system…
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection model. This essentially leads to a bilinear optimal control…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle…
We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…
A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their…