Related papers: A simple intrinsic reduced-observer for geodesic f…
Lagrangian data assimilation aims to recover hidden Eulerian flow fields from sparse, indirect observations of moving tracers. This problem is challenging because tracer trajectories are nonlinearly coupled with the underlying flow, making…
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular…
The log-homotopy particle flow filter resolves the Bayesian update by transporting particles along a continuous trajectory in pseudo-time. However, the governing partial differential equation for the flow velocity is fundamentally…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…
This paper is the third and final component of a three-part effort on observers contracting a Riemannian distance between the state of the system and its estimate. In Part I, we showed that such a contraction property holds if the system…
We interpret the Lorentz force equation as a geodesic equation associated with a non-linear connection. Using a geometric averaging procedure, we prove that for narrow and smooth one-particle distribution functions whose supports are…
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…
In this article we consider the ergodic optimization for hyperbolic flows and Lorenz attractors with respect to both continuous and Holder continuous observables. In the context of hyperbolic flows we prove that a Baire generic subset of…
We present the first solution to the problem of estimation of the state of multimachine power systems with lossy transmission lines. We consider the classical three-dimensional \fluxdecay" model of the power system and assume that the…
We introduce and study the Chaplygin systems with gyroscopic forces. This natural class of nonholonomic systems has not been treated before. We put a special emphasis on the important subclass of such systems with magnetic forces. The…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an ele- mentary proof to the known rigidity results for…
The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed…
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions…
This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…
The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained…
The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which…