Related papers: On Dimension Varying Control Systems: A Universal …
A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state-space manifold $M$ of a given control system into some Euclidean space $\mathbb R^n$, extend the system from…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
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…
Landmark manifolds consist of a collection of distinct points, and dynamics on this manifold can be used to represent flows, such as solutions of ODEs and flows deforming a shape. We will consider landmark configurations in the Euclidean…
In this article, we investigate the problem of simultaneously steering an uncountable family of finite dimensional time-varying linear systems. We call this class of control problems Ensemble Control, a notion coming from the study of spin…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…
If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…
In this paper we describe a combined combinatorial/numerical approach to studying equilibria and bifurcations in network models arising in Systems Biology. ODE models of the dynamics suffer from high dimensional parameters which presents a…
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper…
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum…
This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show…
Manipulation of infinite dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem…
Consider a Hamiltonian system of type \[ -\Delta u=H_{v}(u,v),\ -\Delta v=H_{u}(u,v) \ \ \text{ in } \Omega, \qquad u,v=0 \text{ on } \partial \Omega \] where $H$ is a power-type nonlinearity, for instance $H(u,v)= |u|^p/p+|v|^q/q$, having…
In this work some aspects of models with universal extra dimensions are studied. In particular, in the case of models with one universal extra dimension their phenomenology is investigated and used to extract bounds on the size of the extra…
An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control.…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…