Input shaping control with reentry commands of prescribed duration

Control of flexible mechanical structures often deals with the problem of unwanted vibration. The input shaping is a feedforward method based on modification of the input signal so that the output performs the demanded behaviour. The presented approach is based on a finite-time Laplace transform. It leads to no-vibration control signal without any limitations on its time duration because it is not strictly connected to the system resonant frequency. This idea used for synthesis of control input is extended to design of dynamical shaper with reentry property that transform an arbitrary input signal to the signal that cause no vibration. All these theoretical tasks are supported by the results of simulation experiments

Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions

We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2)_L x U(1)_Y theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The `would-be' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.Comment: 11 pages, REVTeX4, 10 eps figures; additional remarks and references added; version published in Phys. Rev.

Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.Comment: Accepted at ICTAC 201

On Refinements of Boolean and Parametric Modal Transition Systems

We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes. Firstly, we reduce the problem of modal refinement over both classes to a problem solvable by a QBF solver and provide experimental results showing our technique scales well. Secondly, we extend the algorithm for thorough refinement of MTS providing better complexity then via reductions to previously studied problems. Finally, we investigate the relationship between modal and thorough refinement on the two classes and show how the thorough refinement can be approximated by the modal refinement

Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory

There are two fundamentally different approaches to specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations. In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. We also introduce a new operation of quotient for the above equivalent formalisms, which is adjoint to structural composition and allows synthesis of missing specifications from partial implementations. This is a substantial generalisation of the quotient for deterministic modal transition systems defined in earlier papers

Relative Value Iteration for Stochastic Differential Games

We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for the ergodic game and characterize the optimal stationary strategies. The data is not assumed to be bounded, nor do we assume geometric ergodicity. Thus our results extend previous work in the literature. We also study a relative value iteration scheme that takes the form of a parabolic Isaac's equation. Under the hypothesis of geometric ergodicity we show that the relative value iteration converges to the elliptic Isaac's equation as time goes to infinity. We use these results to establish convergence of the relative value iteration for risk-sensitive control problems under an asymptotic flatness assumption

Dynamical electroweak symmetry breaking due to strong Yukawa interactions

We present a new mechanism for electroweak symmetry breaking (EWSB) based on a strong Yukawa dynamics. We consider an SU(2)_L x U(1)_Y gauge invariant model endowed with the usual Standard model fermion multiplets and with two massive scalar doublets. We show that, unlike in the Standard model, EWSB is possible even with vanishing vacuum expectation values of the scalars. Such EWSB is achieved dynamically by means of the (presumably strong) Yukawa couplings and manifests itself by the emergence of fermion and gauge boson masses and scalar mass-splittings, which are expressed in a closed form in terms of the fermion and scalar proper self-energies. The `would-be' Nambu--Goldstone bosons are shown to be composites of both the fermions and the scalars. We demonstrate that the simplest version of the model is compatible with basic experimental constraints.Comment: 6 pages, REVTeX4, 3 eps figures; discussion of compatibility with EW precision data added; version published in J. Phys.

Eternal solutions to a singular diffusion equation with critical gradient absorption

The existence of nonnegative radially symmetric eternal solutions of exponential self-similar type $u(t,x)=e^{-p\beta t/(2-p)} f_\beta(|x|e^{-\beta t};\beta)$ is investigated for the singular diffusion equation with critical gradient absorption \begin{equation*} \partial_{t} u-\Delta_{p} u+|\nabla u|^{p/2}=0 \quad \;\;\hbox{in}\;\; (0,\infty)\times\real^N \end{equation*} where $2N/(N+1) < p < 2$. Such solutions are shown to exist only if the parameter $\beta$ ranges in a bounded interval $(0,\beta_*]$ which is in sharp contrast with well-known singular diffusion equations such as $\partial_{t}\phi-\Delta_{p} \phi=0$ when $p=2N/(N+1)$ or the porous medium equation $\partial_{t}\phi-\Delta\phi^m=0$ when $m=(N-2)/N$. Moreover, the profile $f(r;\beta)$ decays to zero as $r\to\infty$ in a faster way for $\beta=\beta_*$ than for $\beta\in (0,\beta_*)$ but the algebraic leading order is the same in both cases. In fact, for large $r$, $f(r;\beta_*)$ decays as $r^{-p/(2-p)}$ while $f(r;\beta)$ behaves as $(\log r)^{2/(2-p)} r^{-p/(2-p)}$ when $\beta\in (0,\beta_*)$

On the speed of convergence to stationarity of the Erlang loss system

We consider the Erlang loss system, characterized by $N$ servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of $N.$ We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates