Anthony M. Bloch
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View article: Dynamic sensor selection for biomarker discovery
Dynamic sensor selection for biomarker discovery Open
Recent advances in biotechnologies enable monitoring of biological systems with unprecedented resolution, yet identifying and interpreting biological signals remains a major challenge in clinical and research settings. Classically, biomark…
View article: Learning Hybrid Dynamics via Convex Optimizations
Learning Hybrid Dynamics via Convex Optimizations Open
This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear …
View article: Virtual nonlinear nonholonomic constraints from a symplectic point of view
Virtual nonlinear nonholonomic constraints from a symplectic point of view Open
In this paper, we provide a geometric characterization of virtual nonlinear nonholonomic constraints from a symplectic perspective. Under a transversality assumption, there is a unique control law making the trajectories of the associated …
View article: Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints
Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints Open
In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…
View article: Dynamic Sensor Selection for Biomarker Discovery.
Dynamic Sensor Selection for Biomarker Discovery. Open
Advances in methods of biological data collection are driving the rapid growth of comprehensive datasets across clinical and research settings. These datasets provide the opportunity to monitor biological systems in greater depth and at fi…
View article: Integrable sub-Riemannian geodesic flows on the special orthogonal group
Integrable sub-Riemannian geodesic flows on the special orthogonal group Open
We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metric defined on this distribution are completely integrable. O…
View article: Nonholonomic mechanics and virtual constraints on Riemannian homogeneous spaces
Nonholonomic mechanics and virtual constraints on Riemannian homogeneous spaces Open
Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution associated with an affine connection mechanical control sys…
View article: Geometric stabilization of virtual linear nonholonomic constraints
Geometric stabilization of virtual linear nonholonomic constraints Open
In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic constraint that is control invariant via the same feedback cont…
View article: Learning Nonholonomic Dynamics with Constraint Discovery
Learning Nonholonomic Dynamics with Constraint Discovery Open
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints…
View article: A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization
A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization Open
This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via…
View article: Geometric Aspects of Observability of Hypergraphs
Geometric Aspects of Observability of Hypergraphs Open
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and unamb…
View article: Symmetric Discrete Optimal Control and Deep Learning
Symmetric Discrete Optimal Control and Deep Learning Open
We analyze discrete optimal control problems and their connection with back propagation and deep learning. We consider in particular the symmetric representation of the discrete rigid body equations developed via optimal control analysis a…
View article: The Interplay Between Symmetries and Impact Effects on Hybrid Mechanical Systems
The Interplay Between Symmetries and Impact Effects on Hybrid Mechanical Systems Open
Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to define two classes of impacts for the discrete-time transition o…
View article: Generalized Models for Inflationary Preheating: Oscillations and Symmetries
Generalized Models for Inflationary Preheating: Oscillations and Symmetries Open
The paradigm of the inflationary universe provides a possible explanation for several observed cosmological properties. In order for such solutions to be successful, the universe must convert the energy stored in the inflaton potential int…
View article: Geometric Aspects of Observability of Hypergraphs
Geometric Aspects of Observability of Hypergraphs Open
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and unamb…
View article: Virtual Constraints on Lie groups
Virtual Constraints on Lie groups Open
This paper studies virtual constraints on Lie groups. Virtual constraints are invariant relations imposed on a control system via feedback. In this work, we introduce the notion of \textit{virtual constraints on Lie groups}, in particular,…
View article: Completeness of Riemannian metrics: an application to the control of constrained mechanical systems
Completeness of Riemannian metrics: an application to the control of constrained mechanical systems Open
We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems. In essence our result is based on the construction of a …
View article: Optimal Control with Obstacle Avoidance for Incompressible Ideal Flows of an Inviscid Fluid
Optimal Control with Obstacle Avoidance for Incompressible Ideal Flows of an Inviscid Fluid Open
It has been shown in previous works that an optimal control formulation for an incompressible ideal fluid flow yields Euler's fluid equations. In this paper we consider the modified Euler's equations by adding a potential function playing …
View article: On the Geometry of Virtual Nonlinear Nonholonomic Constraints
On the Geometry of Virtual Nonlinear Nonholonomic Constraints Open
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints …
View article: HAT: Hypergraph analysis toolbox
HAT: Hypergraph analysis toolbox Open
Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilize…
View article: Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics
Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics Open
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupl…
View article: Symmetric Toda, gradient flows, and tridiagonalization
Symmetric Toda, gradient flows, and tridiagonalization Open
The Toda lattice (1967) is a Hamiltonian system given by $n$ points on a line governed by an exponential potential. Flaschka (1974) showed that the Toda lattice is integrable by interpreting it as a flow on the space of symmetric tridiagon…
View article: Observability of Hypergraphs
Observability of Hypergraphs Open
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
View article: Virtual Affine Nonholonomic Constraints
Virtual Affine Nonholonomic Constraints Open
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
View article: Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints
Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints Open
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists i…
View article: Virtual Nonholonomic Constraints: A Geometric Approach
Virtual Nonholonomic Constraints: A Geometric Approach Open
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the velocitie…
View article: Lie Algebraic Cost Function Design for Control on Lie Groups
Lie Algebraic Cost Function Design for Control on Lie Groups Open
This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to …