scholarly journals State Feedback of Complex Systems Using Fuzzy Cognitive Maps

2018 ◽  
Vol 6 (3) ◽  
pp. 1-6 ◽  
Author(s):  
Vassiliki Mpelogianni ◽  
Ioannis Arvanitakis ◽  
Peter Groumpos
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
State Space ◽  
State Vector ◽  
State Feedback ◽  
Mathematical Formulation ◽  
Cognitive Maps ◽  
The State ◽  
Fuzzy Cognitive Maps ◽  
System Model

Complex systems have become a research area with increasing interest over the last years. The emergence of new technologies, the increase in computational power with reduced resources and cost, the integration of the physical world with computer based systems has created the possibility of significantly improving the quality of life of humans. While a significant degree of automation within these systems exists and has been provided in the past decade with examples of the smart homes and energy efficient buildings, a paradigm shift towards autonomy has been noted. The need for autonomy requires the extraction of a model; while a strict mathematical formulation usually exists for the individual subsystems, finding a complete mathematical formulation for the complex systems is a near impossible task to accomplish. For this reason, methods such as the Fuzzy Cognitive Maps (FCM) have emerged that are able to provide with a description of the complex system. The system description results from empirical observations made from experts in the related subject – integration of expert’s knowledge – that provide the required cause-effect relations between the interacting components that the FCM needs in order to be formulated. Learning methods are employed that are able to improve the formulated model based on measurements from the actual system. The FCM method, that is able to inherently integrate uncertainties, is able to provide an adequate model for the study of a complex system. With the required system model, the next step towards the development of a autonomous systems is the creation of a control scheme. While FCM can provide with a system model, the system representation proves inadequate to be utilized to design classic model based controllers that require a state space or frequency domain representation. In state space representation, the state vector contains the variables of the system that can describe enough about the system to determine its future behavior in absence of external variables. Thus, within the components – the nodes of the FCM, ideally those can be identified that constitute the state vector of the system. In this work the authors propose the creation of a state feedback control law of complex systems via Fuzzy Cognitive Maps. Given the FCM representation of a system, initially the components-states of the system are identified. Given the identified states, a FCM representation of the controller occurs where the controller parameters are the weights of the cause-effect relations of the system. The FCM of the system then is augmented with the FCM of the controller. An example of the proposed methodology is given via the use of the cart-pendulum system, a common benchmark system for testing the efficiency of control systems.

scholarly journals State Feedback of Complex Systems using Fuzzy Cognitive Maps

2017 ◽  
Author(s):  
Vassiliki Mpelogianni ◽  
Ioannis Arvanitakis ◽  
Peter P. Groumpos
Keyword(s):  
Complex Systems ◽  
State Feedback ◽  
Cognitive Maps ◽  
Fuzzy Cognitive Maps

A Fuzzy Cognitive Maps Modeling, Learning and Simulation Framework for Studying Complex System

2011 ◽  
pp. 243-256 ◽  
Author(s):  
Maikel León ◽  
Gonzalo Nápoles ◽  
Ciro Rodriguez ◽  
María M. García ◽  
Rafael Bello ◽  
...  
Keyword(s):  
Complex System ◽  
Cognitive Maps ◽  
Fuzzy Cognitive Maps ◽  
Simulation Framework

scholarly journals A Stochastic and State Space Model for Tumour Growth and Applications

2009 ◽  
Vol 10 (2) ◽  
pp. 117-138 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Weiming Ke ◽  
G. Webb
Keyword(s):  
State Space ◽  
Stochastic System ◽  
Tumour Growth ◽  
Deterministic Model ◽  
State Space Model ◽  
Tumour Cells ◽  
The State ◽  
System Model ◽  
State Variables ◽  
Space Model

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

FUZZY COGNITIVE MAPS MODEL FOR LARGE SCALE COMPLEX SYSTEMS

2002 ◽  
Vol 35 (1) ◽  
pp. 277-282 ◽  
Author(s):  
C.D. Stylios ◽  
Peter P. Groumpos
Keyword(s):  
Complex Systems ◽  
Large Scale ◽  
Cognitive Maps ◽  
Fuzzy Cognitive Maps

scholarly journals The technology of using fuzzy cognitive maps from a mathematical point of view

2021 ◽  
pp. 1-22
Author(s):  
Yuri Germanovich Rykov
Keyword(s):  
Complex Systems ◽  
System Dynamics ◽  
Cognitive Maps ◽  
Cognitive Map ◽  
Point Of View ◽  
Fuzzy Cognitive Maps ◽  
Generalized System ◽  
Computational Procedures ◽  
The Relationship ◽  
Theoretical Results

A broader view of the technology of fuzzy cognitive maps is described, in which the cognitive map is considered as a carrier of computational procedures. This approach can be described as a generalized system dynamics. This interpretation makes it easier to obtain theoretical results that can characterize the behavior of complex systems. In particular, in the case of simple computational procedures, the relationship between the degree of influence of factors and the structure of the system, namely, the presence of connecting paths and cycles in the corresponding digraph, is clarified.

scholarly journals Management of Information Risks for Complex System Using the «Cognitive Game» Mechanism

2020 ◽  
pp. 2-10
Author(s):  
Andrey Kalashnikov ◽  
◽  
Evgenia Anikina ◽  
Keyword(s):  
Complex System ◽  
Risk Management ◽  
Complex Systems ◽  
Computer Network ◽  
Mutual Influence ◽  
The State ◽  
Theoretic Approach ◽  
Risk Manager ◽  
Game Theoretic ◽  
Local Risk

Purpose of the article: development of mechanisms for solving problems of information risk management of complex systems in conditions of uncertainty and mutual influence of system elements on each other. Research method: game-theoretic mathematical modeling of risk management processes in complex systems based on arbitration schemes and multistep games on cognitive maps. The result: a general model of a complex system (for example, a heterogeneous computer network) is considered, within which the risk manager (risk-manager) carries out effective risk management by distributing the resource at his disposal among its elements (nodes of a computer network). To assess the state of the system elements, functions of local risk are proposed that satisfy certain specified requirements, and to assess the state of the system as a whole, an integral risk function is proposed. It is shown that in the case of independence (absence of mutual influence on each other) of the system elements to find an effective resource allocation, a game-theoretic approach can be used based on an arbitration scheme based on the principles of stimulation and non-suppression (MS-solution). For the case when changes in the level of risk for one element of the system can have a significant impact on the levels of risks of other elements, it is proposed to use game-theoretic models based on the MS-solution and a multistep “cognitive game”.

scholarly journals Cooperation of agents in complex systems based on supervision

2014 ◽  
Vol 14 (1) ◽  
pp. 40-51
Author(s):  
František Čapkovič
Keyword(s):  
Complex Systems ◽  
State Vector ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
The State ◽  
System Structure ◽  
Continuous Systems ◽  
Production Lines ◽  
Supervisor Synthesis

Abstract Complex systems consist of many cooperating devices. To have a transparent view on the system structure, as well as on the structural interconnections and cooperation of the subsystems, it is useful to synthesize the complex systems systematically in a prescribed order, even in analytical terms (if possible). The supervision of the subsystems seems to be a very suitable approach to accomplish these demands, and consequently it makes the complex systems diagnostics easier. The substantial agents (i.e., the agents of material nature − e.g., devices like particular production lines, robots, numerically controlled machines, etc.) can be coordinated and forced to cooperation by means of efficiently synthesized supervisors. The cooperation process has the character of DES (Discrete-Event Systems), because any system (including continuous systems), has minimally two discrete states - idle and working. DES control theory can be successfully utilized in supervisor synthesis. There are several approaches to modeling the agents and the process of supervisor synthesis. The Petri net-based approach is one of them. Place/Transition Petri Nets (P/T PN) are used here for modeling the behaviour of particular agents, as well as in the computational parocess used for the supervisor synthesis. Two main methods of the P/T PN-based supervision will be used, namely (i) the supervision based on the place invariants (P-invariants) of P/T PN, utilizing only the state vector during the supervisor synthesis, and (ii) the extended supervision utilizing not only the state vector, but also the control vector and Parikh’s vector. The efficiency of the proposed approach is illustrated in a case study.

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