Evolving Granular Fuzzy Model-Based Control of Nonlinear Dynamic Systems

Abstract

Unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process. The purpose is to stabilize the closed-loop system under changes of the operating conditions and process parameters. This paper introduces a model-based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention. An incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams. State feedback control laws and closedloop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy Lyapunov function. Bounded control inputs are also taken into account in the control system design. We explain the role of fuzzy granular data and the use of parallel distributed compensation. Fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge. Although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown, for expositional clarity, we consider online modeling and stabilization of the well-known Lorenz chaos as an illustrative example.

MSAFIS: an evolving fuzzy inference system

“…The same authors [21] adopt a granular fuzzy control approach as a step toward the development of a more general framework for online modeling and control of unknown non-stationary processes with no human intervention. The work described in [23] suggests an enhanced version of the evolving participatory learning approach which includes both a utility measure to shrink rule bases and a variable cluster radius mechanism to improve the cluster structure.…”

A Review on Evolving Interval and Fuzzy Granular Systems

“…Evolving granular modeling [53,54] [70] [89][90][91][92][93][94][95] comes not only as an approach to capture the essence of stream data but also as a framework to extrapolate spatio-temporal correlations from lower-level raw data and provide a more abstract humanlike representation of them. Research effort into granular computing toward online environment-related tasks is supported by a manifold of relevant applications such as financial, health care, video and image processing, GPS navigation, click stream analysis, online information security, process control, etc.…”

Linearização por realimentação granular robusta com algoritmo evolutivo Takagi-Sugeno: Análise e avaliação de desempenho

“…Baseando-se na teoria de sistemas fuzzy, (Wang and Mendel, 1992) desenvolveram um algoritmo usando princípio dos mínimos quadrados recursivos para construir uma base de regras fuzzy. Conforme (Park and Park, 2003), as propriedades desse algoritmo possibilitaram que outros autores desenvolvessem arquiteturas de controle adaptativas fuzzy para sistemas não lineares (Souza et al, 2012), (Silva et al, 2013), (Leite et al, 2015). Nessa linha têm-se, por exemplo, o controle adaptativo fuzzy indireto que estima a dinâmica e o sinal de controle da malha fechada (Wang, 1996), (Banerjee et al, 2011), (Park et al, 2003).…”