相关论文: Saddle Flow Dynamics: Observable Certificates and …

Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…

Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…

This work establishes a crucial step toward advancing data-driven trajectory-based methods for stochastic systems with unknown mathematical dynamics. In contrast to scenario-based approaches that rely on independent and identically…

Safety is the major consideration in controlling complex dynamical systems using reinforcement learning (RL), where the safety certificate can provide provable safety guarantee. A valid safety certificate is an energy function indicating…

The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw…

Estimating continuous optical flow is a fundamental yet challenging problem in dynamic visual perception. Event-based cameras, with microsecond latency and high dynamic range, capture brightness changes asynchronously, offering a unique…

This paper presents a data-driven approach for jointly learning a robust full-state observer and its robustness certificate for systems with unknown dynamics. Leveraging incremental input-to-state stability (delta ISS) notions, we jointly…

We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that…

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla…

Robot motion distributions often exhibit multi-modality and require flexible generative models for accurate representation. Streaming Flow Policies (SFPs) have recently emerged as a powerful paradigm for generating robot trajectories by…

Ensuring safe autonomous driving in the presence of occlusions poses a significant challenge in its policy design. While existing model-driven control techniques based on set invariance can handle visible risks, occlusions create latent…

We describe all possible topological structures of Morse-Smale flows without closed trajectories on a three-dimensional sphere, which have two sources, two sinks, one saddle of Morse index 1, one saddle of Morse index 2, and no more than 10…

We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point…

Safety-critical control tasks with high levels of uncertainty are becoming increasingly common. Typically, techniques that guarantee safety during learning and control utilize constraint-based safety certificates, which can be leveraged to…

In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…

Control design for general nonlinear robotic systems with guaranteed stability and/or safety in the presence of model uncertainties is a challenging problem. Recent efforts attempt to learn a controller and a certificate (e.g., a Lyapunov…

Significant advancements have emerged in the theory of asymptotic stability of shear flows in stably stratified fluids. In this comprehensive review, we spotlight these recent developments, with particular emphasis on novel approaches that…

A flow decomposition method based on canonical correlation analysis is proposed in this paper to optimally dissect complex flows into mutually orthogonal modes that are ranked by their cross-correlation with an observable. It is…