相关论文: Stabilizing Radial Basis Function Methods for Cons…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
We study extremal shocks of $1$-d hyperbolic systems of conservation laws which fail to be genuinely nonlinear. More specifically, we consider either $1$- or $n$-shocks in characteristic fields which are either concave-convex or…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
We investigate the Ising model on finite subgraphs of the hyperbolic lattice under minus boundary conditions and in the presence of a positive external field $h$. Interpreting the boundary as frozen or cold wall conditions, we show that,…
Kinetic relations are required in order to characterize nonclassical undercompressive shock waves and formulate a well-posed initial value problem for nonlinear hyperbolic systems of conservation laws. Such nonclassical waves arise in weak…
This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence…
We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…
Control barrier functions (CBFs) offer a powerful tool for enforcing safety specifications in control synthesis. This paper deals with the problem of constructing valid CBFs. Given a second-order system and any desired safety set with…
Measurements and state estimates are often imperfect in control practice, posing challenges for safety-critical applications, where safety guarantees rely on accurate state information. In the presence of estimation errors, several prior…
We propose control barrier functions (CBFs) for a family of dynamical systems to satisfy a broad fragment of Signal Temporal Logic (STL) specifications, which may include subtasks with nested temporal operators or conflicting requirements…
The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite…
Control barrier functions (CBFs) are a popular tool for safety certification of nonlinear dynamical control systems. Recently, CBFs represented as neural networks have shown great promise due to their expressiveness and applicability to a…
Using control barrier functions (CBFs) as safety filters provides a computationally inexpensive yet effective method for constructing controllers in safety-critical applications. However, using CBFs requires the construction of a valid CBF,…
Applications that require multi-robot systems to operate independently for extended periods of time in unknown or unstructured environments face a broad set of challenges, such as hardware degradation, changing weather patterns, or…
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary…
Control Barrier Functions (CBFs) have emerged as a powerful paradigm in control theory, providing a principled approach to enforcing safety-critical constraints in dynamic systems. This survey paper comprehensively explores the foundational…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.