Stabilization of Recurrent Fuzzy Systems via Sum of Squares-based Hybrid Control

This paper presents an approach for stabilization of equilibria in recurrent fuzzy systems. This type of dynamic fuzzy systems being defined via linguistic rules can be interpreted as interpolation between constant gradients, and therefore as hybrid dynamical system. It is shown that the latter viewpoint allows for a precise description of the system dynamics, but on the other hand lacks transparency. In order to render a given equilibrium of the recurrent fuzzy system globally asymptotically stable, local polynomial controllers are computed via sum of squares optimization to allow only for deterministic mode transitions on a micro level. In addition, the controlled recurrent fuzzy system can then be interpreted as finite deterministic automaton, thus allowing for analysis of system properties on a more abstract macro level. Relaxations are proposed in cases where recurrent fuzzy systems may not be rendered deterministic and the method is applied to two examples

Parallel Distributed Compensation for Piecewise Bilinear Models and Recurrent Fuzzy Systems Based on Piecewise Quadratic Lyapunov Functions

Piecewise Bilinear Models and Recurrent Fuzzy Systems are universal approximators for any smooth nonlinear dynamics. One of their advantage is the efficient representation of the modeled system dynamics by means of rule-bases or look-up-tables. In this paper, it is shown how to obtain provably stabilizing controllers by means of piecewise quadratic Lyapunov functions. Interpolating controllers with affine local controllers are considered for interpolation, akin to the concept of parallel distributed compensation widely used for control of Takagi-Sugeno systems

Hedgehog signaling via a calcitonin receptor-like receptor can induce arterial differentiation independently of VEGF signaling in zebrafish

Multiple signaling pathways control the specification of endothelial cells (ECs) to become arteries or veins during vertebrate embryogenesis. Current models propose that a cascade of Hedgehog (Hh), vascular endothelial growth factor (VEGF), and Notch signaling acts instructively on ECs to control the choice between arterial or venous fate. Differences in the phenotypes induced by Hh, VEGF, or Notch inhibition suggest that not all of the effects of Hh on arteriovenous specification are mediated by VEGF. We establish that full derepression of the Hh pathway in ptc1;ptc2 mutants converts the posterior cardinal vein into a second arterial vessel that manifests intact arterial gene expression, intersegmental vessel sprouting, and HSC gene expression. Importantly, although VEGF was thought to be absolutely essential for arterial fates, we find that normal and ectopic arterial differentiation can occur without VEGF signaling in ptc1;ptc2 mutants. Furthermore, Hh is able to bypass VEGF to induce arterial differentiation in ECs via the calcitonin receptor-like receptor, thus revealing a surprising complexity in the interplay between Hh and VEGF signaling during arteriovenous specification. Finally, our experiments establish a dual function of Hh during induction of runx1+ HSCs

Feedforward Tracking Control of Flat Recurrent Fuzzy Systems

Flatness based feedforward control has proven to be a feasible solution for the problem of tracking control, which may be applied to a broad class of nonlinear systems. If a flat output of the system is known, the control is often based on a feedforward controller generating a nominal input in combination with a linear controller stabilizing the linearized error dynamics around the trajectory. We show in this paper that the very same idea may be incorporated for tracking control of MIMO recurrent fuzzy systems. Their dynamics is given by means of linguistic differential equations but may be converted into a hybrid system representation, which then serves as the basis for controller synthesis

Synthese von Zustands- und Ausgangsrückführungen für rekurrente Fuzzy-Systeme

Als spezielle Klasse dynamischer Fuzzy-Systeme bieten rekurrente Fuzzy-Systeme die Möglichkeit, dynamische Prozesse anhand von Expertenwissen oder Messdaten zu modellieren. Dabei zeichnet sich die Regelbasis durch die Möglichkeit der linguistischen Interpretierbarkeit und somit der Transparenz aus. Dieser Artikel stellt Ansätze vor, mit denen sowohl (beobachterbasierte) Zustands- als auch Ausgangsrückführungen zur Stabilisierung bekannter Ruhelagen mit Hilfe bilinearer Matrixungleichungen ausgelegt werden können. Die sich ergebenden Regler sind dabei strukturell äquivalent zu Fuzzy-Reglern und können somit ebenfalls linguistisch interpretiert werden. Hinsichtlich der Ausgangsrückführungen wird gezeigt, dass sich bekannte Syntheseansätze aus der linearen Systemtheorie ebenfalls auf Ausgangsrückführungen für rekurrente Fuzzy-Systeme übertragen lassen

The Political Responsiveness of James K. Polk to Public Opinion Regarding the Mexican-American War or A Test of Carfted Talk in the 19th Century

Zusammenfassung Als spezielle Klasse dynamischer Fuzzy-Systeme bieten rekurrente Fuzzy-Systeme die Möglichkeit, dynamische Prozesse anhand von Expertenwissen oder Messdaten zu modellieren. Dabei zeichnet sich die Regelbasis durch die Möglichkeit der linguistischen Interpretierbarkeit und somit der Transparenz aus. Dieser Artikel stellt Ansätze vor, mit denen sowohl (beobachterbasierte) Zustands- als auch Ausgangsrückführungen zur Stabilisierung bekannter Ruhelagen mit Hilfe bilinearer Matrixungleichungen ausgelegt werden können. Die sich ergebenden Regler sind dabei strukturell äquivalent zu Fuzzy-Reglern und können somit ebenfalls linguistisch interpretiert werden. Hinsichtlich der Ausgangsrückführungen wird gezeigt, dass sich bekannte Syntheseansätze aus der linearen Systemtheorie ebenfalls auf Ausgangsrückführungen für rekurrente Fuzzy-Systeme übertragen lassen.</jats:p