Related papers: Mathematical models for geometric control theory
We present a geometric neural network-based tracking controller for systems evolving on matrix Lie groups under unknown dynamics, actuator faults, and bounded disturbances. Leveraging the left-invariance of the tangent bundle of matrix Lie…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
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…
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…
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 provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal…
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
A common goal of quantum control is to maximize a physical observable through the application of a tailored field. The observable value as a function of the field constitutes a quantum control landscape. Previous works have shown, under…
We investigate the use of transformer sequence models as dynamics models (TDMs) for control. We find that TDMs exhibit strong generalization capabilities to unseen environments, both in a few-shot setting, where a generalist TDM is…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…