Related papers: Robust Control with Gradient Uncertainty
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
Uncertainty quantification is one of the central challenges for machine learning in real-world applications. In reinforcement learning, an agent confronts two kinds of uncertainty, called epistemic uncertainty and aleatoric uncertainty.…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…
We introduce a reinforcement learning method for a class of non-Markov systems; our approach extends the actor-critic framework given by Rose et al. [New J. Phys. 23 013013 (2021)] for obtaining scaled cumulant generating functions…
Reinforcement Learning (RL) and its integration with deep learning have achieved impressive performance in various robotic control tasks, ranging from motion planning and navigation to end-to-end visual manipulation. However, stability is…
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…
Driven by inherent uncertainty and the sim-to-real gap, robust reinforcement learning (RL) seeks to improve resilience against the complexity and variability in agent-environment sequential interactions. Despite the existence of a large…
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those equations regards the existence of a lower bound to the…
This paper extends recent results on the exponential performance analysis of gradient based cooperative control dynamics using the framework of exponential integral quadratic constraints ($\alpha-$IQCs). A cooperative source-seeking problem…
We consider control strategies for large-scale interacting agent systems under uncertainty. The particular focus is on the design of robust controls that allow to bound the variance of the controlled system over time. To this end we…
The need for robust control laws is especially important in safety-critical applications. We propose robust hybrid control barrier functions as a means to synthesize control laws that ensure robust safety. Based on this notion, we formulate…
High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. In this paper, we show that through a game played between the uncertainties (or noises) and the controls, adversarial…
We mathematically analyze and numerically study an actor-critic machine learning algorithm for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equations from stochastic control theory. The architecture of the…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time).…
This paper presents several results on performance analysis for a class of uncertain linear quantum systems subject to either quadratic or non-quadratic perturbations in the system Hamiltonian. Also, coherent guaranteed cost controllers are…
The precise implementation and manipulation of quantum gates is key to extracting advantages from future quantum technologies. Achieving this requires very accurate control over the quantum system. If one has complete knowledge about a…
Recent advances in deep reinforcement learning have demonstrated the capability of learning complex control policies from many types of environments. When learning policies for safety-critical applications, it is essential to be sensitive…