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In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
In this article, we study a fractional control problem that models the maximization of the profits obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this…
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…
Battery energy storage is an essential component of a microgrid. The working temperature of the battery is an important factor as a high-temperature condition generally increases losses, reduces useful life, and can even lead to fire…
This paper concerns some time optimal control problems of three different ordinary differential equations in $\mathbb{R}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to…
The problem of designing a profit-maximizing, Bayesian incentive compatible and individually rational mechanism with flexible consumers and costly heterogeneous supply is considered. In our setup, each consumer is associated with a…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
Matrix analysis plays a crucial role in the field of control engineering, providing a powerful mathematical framework for the analysis and design of control systems. This research report explores various applications of matrix analysis in…
In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this article we consider a limit order book model that allows for time-dependent, deterministic depth and resilience of the book and…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
Energy storage applications are explored from a prosumer (consumers with generation) perspective for the island of Madeira in Portugal. These applications could also be relevant to other power networks. We formulate a convex co-optimization…
This paper presents a novel decision-focused framework integrating the physical energy storage model into machine learning pipelines. Motivated by the model predictive control for energy storage, our end-to-end method incorporates the prior…
We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
The high variability of renewable energy resources presents significant challenges to the operation of the electric power grid. Conventional generators can be used to mitigate this variability but are costly to operate and produce carbon…
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
We consider the problem of online learning of optimal control for repeatedly operated systems in the presence of parametric uncertainty. During each round of operation, environment selects system parameters according to a fixed but unknown…
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules…
Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded…