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The entropy regularization is inspired by information entropy from machine learning and the ideas of exploration and exploitation in reinforcement learning, which appears in the control problem to design an approximating algorithm for the…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.
This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…
Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven…
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching…
Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression. A quantitative understanding of…
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…
We prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The…
Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper,…
Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to…
In this note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…