Online self-evolving fuzzy controller with global learning capabilities

Abstract

This paper presents an online self-evolving fuzzy controller with global learning capabilities. Starting from very simple or even empty configurations, the controller learns from its own actions while controlling the plant. It applies learning techniques based on the input/output data collected during normal operation to modify online the fuzzy controller’s structure and parameters. The controller does not need any information about the differential equations that govern the plant, nor any offline training. It consists of two main blocks: a parameter learning block that learns proper values for the rule consequents applying a local and a global strategy, and a self-evolving block that modifies the controller’s structure online. The modification of the topology is based on the analysis of the error surface and the determination of the input variables which are most responsible for the error. Simulation and experimental results are presented to show the controller’s capabilities.

Appendix

The nonlinear servo system used for the experimentation in Sect. 6.2 is modeled by the following differential equations:

$$ \begin{aligned} \dot{{\mathbf{x}}}=& f({\mathbf{x}},u)= A{\mathbf{x}} + Bu + G \\ =& \left[ \begin{array}{ll} 0&1\\ 0&{\frac{-K^2-bR}{RJ}}\\ \end{array}\right]{\mathbf{x}} + \left[ \begin{array}{l} 0\\ {\frac{K}{RJ}} \\ \end{array}\right] u - \left[ \begin{array}{l} 0\\ {\frac{mgl}{J}} \sin(\theta)\\ \end{array}\right]\\ \end{aligned} $$

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where ${\mathbf{x}} = \left[ \begin{array}{ll}\theta&\dot{\theta}\\ \end{array}\right]^T \in {\mathbb{R}}^2$ is the state of the plant, given by the angle θ and the angular velocity $\dot{\theta}$, u is the control input, and G is the gravity term. The plant’s output is the angle θ. The meaning and values of the parameters used for the DC motor are given in Table 4.

Table 4 Nonlinear servo system’s parameters

As mentioned before, the proposed OSEFC does not require the differential equations that govern the plant to be controlled. However, we have included this information in this appendix with the purpose of allowing the interested reader to simulate the experiment.