相关论文: Stabilizing Radial Basis Function Methods for Cons…
We propose a Bayesian framework for feedback boundary control for hyperbolic balance laws. The method propagates a probability distribution over feedback parameters by using Lyapunov decay estimates as a likelihood. In the linear setting,…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
Control barrier functions (CBFs) have emerged as a popular topic in safety critical control due to their ability to provide formal safety guarantees for dynamical systems. Despite their powerful capabilities, the determination of feasible…
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…
In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF)…
This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust…
A particle number conserving BCS approach (FBCS) is formulated in the relativistic mean field (RMF) model. It is shown that the so-obtained RMF+FBCS model can describe the weak pairing limit. We calculate the ground-state properties of the…
In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
To navigate complex environments, robots must increasingly use high-dimensional visual feedback (e.g. images) for control. However, relying on high-dimensional image data to make control decisions raises important questions; particularly,…
The synthesis of Control Barrier Functions (CBFs) often involves demanding computations or a meticulous construction. However, structural properties of the system dynamics and constraints have the potential to mitigate these challenges. In…
This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer…
Control barrier functions (CBFs) play a critical role in the design of safe optimization-based controllers for control-affine systems. Given a CBF associated with a desired ``safe'' set, the typical approach consists in embedding CBF-based…
In this paper we improve the results of \cite{MT} and show that a weak hyperbolic transitivity implies the uniqueness of hyperbolic SRB measures. As an important corollary, it arises the ergodicity of the system in a conservative setting.…
We show that the energy of classical solutions to the wave equation with hyperbolic boundary condition (i.e., dynamic Wentzell boundary condition) and damping on the boundary decays like 1/t. In fact we allow mixed boundary conditions: a…
In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single…
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…
This paper is concerned with the asymptotic stabilities of the inviscid and viscous shocks for the scalar conservation laws on the half-line $(-\infty,0)$ with shock speed $s<0$, subjected to the time-periodic boundary condition, which…