The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system outpu...

In a recent work [8] a numerical method has been proposed to simulate offequilibrium zero-temperature parallel dynamics for the SK model without finite size effects. We study the extension of the method to non-zero temperature and sequential dynamics, and analyze more carefully the involved computational problems. We find evidence, in the glassy phase, for an algebraic relaxation of the energy ...

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has ‘strict and non-positive relative degree’. We present two main results: First, a so called ‘zero dynamics form’ is derived: this form is – within the class of system equival...

For multi-input multi-output (MIMO) linear systems with existing vector relative degree a normal form is constructed. This normal form is not only structural simple but allows to characterize the system’s zero dynamics for the design of feedback controllers. A characterization of the zero dynamics in terms of the normal form is given.

Following the work of Guo, Thompson, and Sewell (Y.Guo, D.L.Thompson, and T.D. Sewell, J.Chem.Phys. 104, 576 (1996)) on the zero point energy correction of classical trajectories, we emphasize that the zero-point energy of a molecule is a quantum phenomenon with no classical counterpart, rooted soundly in the positionmomentum uncertainty principle. As a consequence certain quantum “ingredients,...

In this paper, we present the probably first application of the popular Dynamic Movement Primitives (DMP) approach to the domain of soccer-playing humanoid robots. DMPs are known for their ability to imitate previously demonstrated motions as well as to flexibly adapt to unforeseen changes to the desired trajectory with respect to speed and direction. As demonstrated in this paper, this makes t...

One of the major tasks of playing soccer is kicking the ball. Executing such complex motions is often solved by interpolating keyframes of the entire motion or by using predefined trajectories of the limbs of the soccer robot. In this paper we present a method to generate the trajectory of the kick foot online and to move the rest of the robot’s body such that it is dynamically balanced. To est...

The objective of this paper is to present systematic methods for throwing motion control of underactuated robots. The Pendubot, an underactuated two-link planar robot, is investigated as a dynamic model of the superior limbs for imitation of human throwing motion whose models are fundamentally underactuated in nature. The controller is designed based on input-output linearization and output zer...

Pions and kaons have double nature: the chiral dynamics of Nambu-Goldstone bosons together with the usual string dynamics common to all mesons. To uncover the interplay of both dynamics the effective chiral Lagrangian is derived from the QCD Lagrangian using the Field Correlator Method and the pion self-energy (mass) operator is written explicitly. The latter contains an infinite number of pole...

Given a two-player zero-sum discounted-payoff stochastic game, we introduce three classes of continuous-time best-response dynamics, stopping-time best-response dynamics, closed-loop best-response dynamics, and open-loop best-response dynamics. We show the global convergence of the first two classes to the set of minimax strategy profiles, and the convergence of the last class when the players ...