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1

Behaviour of fractional discrete-time consensus models with delays for summator dynamics

Girejko E., Mozyrska D., Wyrwas M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 4

403--410

EN

The leader-following consensus problem of fractional-order multi-agent discrete-time systems with delays is considered. In the systems, interactions between agents are defined like in Krause and Cucker-Smale models, but the memory is included by taking both the fractional-order discrete-time operator on the left hand side of the nonlinear systems and the delays. Since in practical problems only bounded number of delays can be considered, we study the fractional order discrete-time models with a finite number of delays. The models of opinions under consideration are investigated for single- and double-summator dynamics of discrete-time by means of analytical methods as well as computer simulations.

2

Changing attitude patterns in group decision making process – a socio-technological approach

Falkiewicz D., Hołda M.

Czasopismo Techniczne. Automatyka

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2012

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R. 109, z. 1-AC

29--39

EN

This paper proposes a novel approach to consensus reaching process, which combines a mathematical model and socio-psychological factors. We attempt to correlate two decision support systems: one with the teacher managing the process of reaching consensus within the laboratory groups of individuals, and computer-based system, with mathematical presumptions as for the consistency of the model with the reality of a particular social group.

PL

Przedmiotem niniejszego artykułu jest nowatorskie podejście do procesu osiągania konsensusu, łączące matematyczny model z czynnikami społeczno-psychologicznym. Autorki podjęły się próby skorelowania dwóch systemów wspomagania decyzji: rzeczywistego z nauczycielem zarządzającym procesem osiągania konsensusu w laboratoryjnych grupach studentów, a także informatycznego, którego matematyczne założenia były zgodne z realnymi zachowaniami określonej grupy społecznej.

3

A matrix inequality based design method for consensus problems in multi-agent systems

Zhai G., Okuno S., Imae J., Kobayashi T.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 4

639-646

EN

In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.