Péter L. Várkonyi

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

On the derivation and tuning of phase oscillator models for lamprey central pattern generators

Using phase response curves and averaging theory, we derive phase oscillator models for the lamprey central pattern generator from two biophysically-based segmental models. The first one relies on network dynamics within a segment to produce the rhythm, while the second contains bursting cells. We study intersegmental coordination and show that the former class of models shows more robust behavior over the animal’s range of swimming frequencies. The network-based model can also easily produce approximately constant phase lags along the spinal cord, as observed experimentally. Precise control of phase lags in the network-based model is obtained by varying the relative strengths of its six different connection types with distance in a phase model with separate coupling functions for each connection type. The phase model also describes the effect of randomized connections, accurately predicting how quickly random network-based models approach the determinisitic model as the number of connections increases.

A new algorithm for RNO-INO type tensor product model representation

A recently developed technique of modelling parameter varying dynamical systems is the Tensor Product model representation, where a system is decomposed to convex combination of several parameterinvariant models. Effectiveness and tractability of the representation depends strongly on the type of the applied convex combination. This paper presents an algorithm, which generates a special type of convex combination, the RNO-INO representation. An example is also introduced.

Formation of Sharp Edges and Planar Areas of Asteroids by Polyhedral Abrasion

While the number of asteroids with known shapes has drastically increased over the past few years, little is known on the time-evolution of shapes and the underlying physical processes. Here we propose an averaged abrasion model based on micro-collisions, accounting for asteroids not necessarily evolving toward regular spheroids, rather (depending on the fall-back rate of ejecta) following an alternative path, thus confirming photometry-derived features, e.g., existence of large, relatively flat areas separated by edges. We show that our model is realistic, since the bulk of the collisions falls into this category.

Different affine decomposition of the model of the prototypical aeroelastic wing section by TP model transformation

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into affine model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting affine models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the LTI models of the convex combination. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

Shell geometry and habitat determination in extinct and extant turtles (Reptilia: Testudinata)

Abstract A variety of means, including forelimb proportions and shell bone histology have been used to infer the paleoecology of extinct turtles. However, the height-to-width ratio of the shell (as a one-parameter shell model) has been dismissed because of its unreliability, and more complex aspects of shell geometry have generally been overlooked. Here we use a more reliable, three-parameter geometric model of the shell outline in anterior view as a means to assess turtle paleoecology. The accuracy of predictions of extant turtle ecology based on our three-parameter shell model is comparable to that derived from forelimb proportions when distinguishing between three ecological classes (terrestrial, semiaquatic, and aquatic). Higher accuracy is obtained when distinguishing between two classes (terrestrial and non-terrestrial), because the contours of aquatic and semiaquatic turtles are often very similar. Our model classifies Proterochersis robusta, a stem turtle from the Late Triassic of Germany, as non-terrestrial, and likely semiaquatic. Our method, combined with inferences based on limb proportions, indicates a diverse range of ecotypes represented by Late Triassic stem turtles. This implies that the ecological diversification of stem-group turtles may have been rapid, or that a substantial period of currently cryptic diversification preceded the first fossil appearance of the turtle stem lineage during the Late Triassic.

Mono-monostatic bodies

An apparatus for bidirectional data transmission includes a predominantly stationary part with a data line connected to cause a phase shift of an osicllator signal for transmission to a predominantly mobile part. AC signal components of the oscillator signal received by the mobile part are formed into square wave pulses and a difference between high and low states of the pulses is indicative of a phase shift. During the high and low states, positive signal edges of a second oscillation frequency are counted and compared to one another so that predetermined difference causes a status change on a data output line in the mobile part.

On the Lyapunov stability of quasistatic planar biped robots

We investigate the local motion of a planar rigid body with unilateral constraints in the neighborhood of a two-contact frictional equilibrium configuration on a slope. A new sufficient condition of Lyapunov stability is developed in the presence of arbitrary external forces. Additionally, we construct an example, which is stable against perturbations by infinitesimal forces, but does not possess Lyapunov stability against infinitesimal displacements or impulses. The great difference between previous stability criteria and ours leads to further questions about the nature of the exact stability condition.

Intelligent 3D Car-Body Deformation Modeling

Car body deformation modeling plays a very important role in crash accident analyses, as well as in safe car body design. The determination of the energy absorbed by the deformation and the corresponding Energy Equivalent Speed (EES) can be of key importance in both cases, however their precise determination is a very difficult task. Although, using the results of crash tests, intelligent methods offer an automatic way to model the deformation of the car- body as well as the crash process itself, based on which we can determine the absorbed energy, the before-crash speed of the car, and other important features of crashes. In this paper a modeling technique and an intelligent expert system are introduced which together are able to follow the deformation process of car- bodies in car crashes and to analyze the strength of the different parts without any human intervention, thus can significantly contribute to the improvement of the modeling, (automatic) design, and safety of car-bodies.

On Synchronization and Traveling Waves in Chains of Relaxation Oscillators with an Application to Lamprey CPG

We study chains of relaxation-type neural oscillators with local excitatory coupling. Phase reductions suggest that such networks typically exhibit traveling waves, but relaxation oscillators often synchronize. We examine these behaviors using the phase response and fast threshold modulation (FTM) theories, which respectively describe network behavior for infinitesimally weak and moderate coupling. Surprisingly, the two different approximations yield quantitatively consistent predictions for chains with one-way coupling. Specifically, approaching the relaxation limit, such chains can exhibit waves with vanishing phase differences (i.e., synchrony) propagating in the coupling direction, or waves with persistent phase differences traveling against the coupling direction. These results provide novel support for the finding that caudo-rostral coupling dominates in the lamprey central pattern generator (CPG), and they suggest that recent models may underestimate the role of network effects in burst generation.