Related papers: An optimal-control framework for reaction diffusio…

This paper is concerned with the optimal control of hysteresis-reaction-diffusion systems. We study a control problem with two sorts of controls, namely distributed control functions, or controls which act on a part of the boundary of the…

In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error…

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…

We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…

This paper is concerned with the well-posedness and optimal control problem of a reaction-diffusion system for an epidemic Susceptible-Infected-Recovered-Susceptible (SIRS) mathematical model in which the dynamics develops in a spatially…

In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…

Diffusion-based planning, learning, and control methods present a promising branch of powerful and expressive decision-making solutions. Given the growing interest, such methods have undergone numerous refinements over the past years.…

In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…

Dynamic flux balance analysis of a bioreactor is based on the coupling between a dynamic problem, which models the evolution of biomass, feeding substrates and metabolites, and a linear program, which encodes the metabolic activity inside…

This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…

Predicting the response of an observed system to a known input is a fruitful first step to accurately control the system's dynamics. Despite the recent advances in fully data-driven algorithms, the most interpretable way to reach this goal…

Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…

Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts…

In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical…

We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…

This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate…

Living organisms exhibit remarkable adaptations across all scales, from molecules to ecosystems. We believe that many of these adaptations correspond to optimal solutions driven by evolution, training, and underlying physical and chemical…

Cell heterogeneity plays an important role in patient responses to drug treatments. In many cancers, it is associated with poor treatment outcomes. Many modern drug combination therapies aim to exploit cell heterogeneity, but determining…