Related papers: Equivariant Filter Design for Discrete-time system…
The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented…
Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by…
Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…
Real-world applications of bipedal robot walking require accurate, real-time state estimation. State estimation for locomotion over dynamic rigid surfaces (DRS), such as elevators, ships, public transport vehicles, and aircraft, remains…
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…
Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…
Compared with linear time invariant systems, linear periodic system can describe the periodic processes arising from nature and engineering more precisely. However, the time-varying system parameters increase the difficulty of the research…
Autonomous Underwater Vehicles (AUVs) and Remotely Operated Vehicles (ROVs) are used for a wide variety of missions related to exploration and scientific research. Successful navigation by these systems requires a good localization system.…
The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this…
For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of…
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are…
Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are…
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden…
Condensed matter physics increasingly focuses on exploiting the magnetic order parameter orientation n as a tuning knob for properties of collinear magnetic materials, but a general method for constructing effective Hamiltonians with…
Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural…
In this paper, we consider the analysis and control of continuous-time nonlinear systems to ensure universal shifted stability and performance, i.e., stability and performance w.r.t. each forced equilibrium point of the system. This…
We present a proof-of-principle implementation of the first fully covariant filtering scheme applied to relativistic fluid turbulence. The filtering is performed with respect to special observers, identified dynamically as moving with the…
Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…