相关论文: Quotients of Invariant Control Systems
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
Coupled gyrostat low-order models (GLOMs) are energy-conserving cores of Galerkin-truncated fluid and geophysical systems, including Rayleigh-Benard convection and vorticity dynamics. A single gyrostat always possesses two quadratic…
Swarm and constellation reconfiguration can be viewed as motion of an unordered point configuration in an ambient space. Here, we provide persistence-stable, symmetry-invariant geometric representations for comparing and monitoring…
The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent…
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only…
Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\alpha) \approx \mathrm{Sl}(2,\mathbb{C}) $ generated by the $\exp \mathfrak{g}_{\pm \alpha}$, where…
Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is…
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…
This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…
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…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Understanding the impact of grid-following (GFL) converters on system frequency dynamics is crucial, from both the center of inertia (COI) and frequency spatial variation perspectives. Part I of this series clarifies the mechanisms by which…
We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and…
We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible $0$-form symmetries. These symmetries can arise as…
High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance…
In this paper we consider reduction of the stochastic Hamilton-Pontryagin principle formulated on the Pontryagin bundle of a manifold $Q$. We prove that a stochastic action invariant under the free and proper action of a Lie group $G$ drops…
In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to…
The purpose of this paper is to develop a model reduction theory for linear quantum stochastic systems that are commonly encountered in quantum optics and related fields, modeling devices such as optical cavities and optical parametric…
The aim of this work is to study the quotients for the diagonal action of SL_3(C) on the product of n-fold of \mathbb{P}^2(C): we are interested in describing how the quotient changes when we vary the polarization (i.e. the choice of an…