Related papers: Quotients of Invariant Control Systems
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…
This paper deals with a general method for the reduction of quantum systems with symmetry. For a Riemannian manifold M admitting a compact Lie group G as an isometry group, the quotient space Q = M/G is not a smooth manifold in general but…
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…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
We study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless)…
We consider a class of dynamical systems on a Lie group $G$ with a left-invariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
We study feedback control for discrete-time linear time-invariant systems in the presence of quantization both in the control action and in the measurement of the controlled variable. While in some application the quantization effects can…
Reaction-diffusion equations are ubiquitous in various scientific domains and their patterns represent a fascinating area of investigation. However, many of these patterns are unstable and therefore challenging to observe. To overcome this…
The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…
This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is…
In contrast to the Euler-Poincar{\'e} reduction of geodesic flows of left- or right-invariant metrics on Lie groups to the corresponding Lie algebra (or its dual), one can consider the reduction of the geodesic flows to the group itself.…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive…
In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \cite{baspinar}, which presents a precise geometric framework in which the primary visual cortex $V1$…