相关论文: "Good Lie Brackets" for Control Affine Systems

This paper presents a novel, Fourier series based numerical method of open-loop control optimization. Due to its flexible assumptions, it can be applied in a large variety of systems, including discontinuous ones or even so-called black…

This thesis focuses on the Lie-theoretic foundations of controlled open quantum systems. We describe Markovian open quantum system evolutions by Lie semigroups, whose corresponding infinitesimal generators lie in a special type of convex…

The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the…

Let Aff(X) be the group of affine diffeomorphisms of a closed homogeneous manifold X=G/B admitting a G-invariant Lebesgue-Haar probability measure $\mu$. For $f_0\in$ Aff(X), let $Z^\infty(f_0)$ be the group of $C^\infty$ diffeomorphisms of…

Let G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits…

We study in detail the operad controlling several pre-Lie algebra structures sharing the same Lie bracket. Specifically, we show that this operad admits a combinatorial description similar to that of Chapoton and Livernet for the pre-Lie…

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…

Let $\mathfrak q=Lie Q$ be an algebraic Lie algebra of index 1, i.e., a generic $Q$-orbit on $\mathfrak q^*$ has codimension 1. We show that the following conditions are equivalent: $\mathfrak q$ is contact; a generic $Q$-orbit on…

In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…

In this paper, we give a control approach to follow a trajectory for a Dubins car controlling the heading independently. The difficulty is that the Dubins car should have a heading corresponding to the argument of the vector speed of the…

Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable…

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC)…

In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid ${\mathcal A}$. We…

We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…