Related papers: On Dimension Varying Control Systems: A Universal …
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
Dynamic evolution behaviors of dimension-varying control systems often appear in the genetic regulatory network and the vehicle clutch system etc. An interesting and significant study on dimension-varying control systems is how to realize…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…
Starting from the vector multipliers, the inner product, norm, distance, as well as addition of two vectors of different dimensions are proposed, which makes the spaces into a topological vector space, called the Euclidean space of…
In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…
A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…
We study the controlled dynamics of the {\it ensembles of points} of a Riemannian manifold $M$. Parameterized ensemble of points of $M$ is the image of a continuous map $\gamma:\Theta \to M$, where $\Theta$ is a compact set of parameters.…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on…
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these…
In this paper, we study uniform ensemble controllability (UEC) of linear ensemble systems defined in an infinite-dimensional space through finite-dimensional settings. Specifically, with the help of the Stone-Weierstrass theorem for…
We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.
Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded…