Related papers: "Good Lie Brackets" for Control Affine Systems

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control using relaxation parameters…

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra and the associated group of characters. For f=Id\_V, we find…

We study an optimal control problem arising from a generalization of rock-paper-scissors in which the number of strategies may be selected from any positive odd number greater than 1 and in which the payoff to the winner is controlled by a…

The linearized double shuffle Lie algebra $\mathfrak{ls}$ is a well-studied Lie algebra, which reflects the depth-graded structure of multiple zeta values. We introduce a generalization $\mathfrak{lq}$, which is motivated from the…

The dynamical systems having both bosonic and fermionic variables play an important role in the theory of supersymmetry. This article addresses the control problems including both bosonic and fermionic variables on Lie supergroup as the…

We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is…

Any Lie group G acting on a Euclidean nonvoid open subset M can be seen as a subgroup of the smooth diffeomorphisms Diff^\infty(M,M) of M into itself. Thus actions by such Lie groups G correspond to smooth coordinate transforms on M which,…

A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold $M$ described by a $t$-dependent vector field $X=\sum_{\alpha=1}^rg_\alpha X_\alpha$, where $X_1,\ldots,X_r$ are vector fields on…

We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by means of frictionless constraints. This leads to a system of…

In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We…

In this paper we extend the results on controllability of linear systems obtained in "Controllability of linear systems on solvable Lie groups", from solvable Lie groups to Lie groups with finite semisimple center.

We derive the equations of motion describing the feedback control of quantum systems in the regime of "good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum…

For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…

We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…

This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…

For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with…