Related papers: The Infinite-Dimensional Standard and Strict Bound…

The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…

We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…

Deep reinforcement learning (RL) is a data-driven, model-free method capable of discovering complex control strategies for macroscopic objectives in high-dimensional systems, making its application towards flow control promising. Many…

It is not hard to prove that a uniformly continuous real function, whose integral up to infinity exists, vanishes at infinity, and it is probably little known that this statement runs under the name "Barbalat's Lemma." In fact, the latter…

Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the…

We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…

Reinforcement learning (RL) has demonstrated impressive performance in various areas such as video games and robotics. However, ensuring safety and stability, which are two critical properties from a control perspective, remains a…

In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical, as failure to do so can lead to catastrophic outcomes. Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate…

While reinforcement learning (RL) has made great advances in scalability, exploration and partial observability are still active research topics. In contrast, Bayesian RL (BRL) provides a principled answer to both state estimation and the…

This paper discusses the \( H_2/H_{\infty} \) control problem for continuous-time mean-field linear stochastic systems with affine terms over a finite horizon. We employ the Mean-Field Stochastic Bounded Real Lemma (MF-SBRL), which provides…

This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on…

We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is…

In this paper, a deep reinforcement learning (DRL)-based approach to the Lyapunov optimization is considered to minimize the time-average penalty while maintaining queue stability. A proper construction of state and action spaces is…

Some recent papers have extended the concept of finite-time stability (FTS) to the context of 2D linear systems, where it has been referred to as finite-region stability (FRS). FRS methodologies make even more sense than the classical FTS…

This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability…

In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…

Physics-informed neural solvers offer a promising route to model-based reinforcement learning in continuous time, where optimal feedback synthesis is governed by Hamilton--Jacobi--Bellman (HJB) equations. Practical implementations often…

In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a…

This paper explores continuous-time control synthesis for target-driven navigation to satisfy complex high-level tasks expressed as linear temporal logic (LTL). We propose a model-free framework using deep reinforcement learning (DRL) where…