Related papers: Equivariant Systems Theory and Observer Design
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws…
A method of designing observers and observer-based tracking controllers is proposed for nonlinear systems on manifolds via embedding into Euclidean space and transversal stabilization. Given a system on a manifold, we first embed the…
Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular…
This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their…
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…
In this work we introduce group-equivariant self-attention models to address the problem of explainable radio galaxy classification in astronomy. We evaluate various orders of both cyclic and dihedral equivariance, and show that including…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
Onboard visual sensing has been widely used in the unmanned ground vehicle (UGV) and/or unmanned aerial vehicle (UAV), which can be modeled as dynamic systems on SE(3). The onboard sensing outputs of the dynamic system can usually be…
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations…
The problem of finite/fixed-time cooperative state estimation is considered for a class of quasilinear systems with nonlinearities satisfying a H\"older condition. A strongly connected nonlinear distributed observer is designed under the…
Due to large variations in shape, appearance, and viewing conditions, object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories,…
We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…
This paper introduces the concept of a synchronous model as an extension of the internal model concept used in observer design for dynamical systems. A system is said to contain a synchronous model of another if there is a suitable error…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…