Incremental Learning and State-Space Evolving Fuzzy Control of Nonlinear Time-Varying Systems with Unknown Model

TL;DR

This paper introduces an incremental, evolving fuzzy control method for unknown nonlinear, time-varying systems, combining granular machine learning and Lyapunov-based real-time gain redesign to achieve stable control.

Contribution

It proposes a novel State-Space Fuzzy-set-Based evolving Modeling approach that adapts from data streams for nonlinear system control.

Findings

Successful one-step prediction of Henon chaos

Achieved asymptotic stabilization of nonlinear systems

Real-time local gain redesign from fuzzy Lyapunov functions

Abstract

We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space Fuzzy-set-Based evolving Modeling (SS-FBeM) approach. The resulting fuzzy model is structurally and parametrically developed from a data stream with focus on memory and data coverage. The fuzzy controller also evolves, based on the data instances and fuzzy model parameters. Its local gains are redesigned in real-time -- whenever the corresponding local fuzzy models change -- from the solution of a linear matrix inequality problem derived from a fuzzy Lyapunov function and bounded input conditions. We have shown one-step prediction and asymptotic stabilization of the Henon chaos.