Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the plant constitutes a piece-wise linear approximation of the nonlinear system and each neuron represents a local linear model for which a linear controller is designed. The neural gas model works as an observer and a controller at the same time. A state feedback control is implemented by estimation of the state variables based on the local transfer function that was provided by the local linear model. The gradient vectors obtained by the supervised neural gas algorithm provide a robust procedure for feedforward nonlinear control, that is, supposing the inexistence of disturbances. See:

Iván Machón-González and Hilario López-García, “Feedforward Nonlinear Control Using Neural Gas Network,” Complexity, vol. 2017, Article ID 3125073, 11 pages, 2017. doi:10.1155/2017/3125073.

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The algorithm in Matlab source code is available for download here.

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Área de Ingeniería de Sistemas y Automática

setpoint (Green color)

Output (controlled variable) (blue color)

control action (blue color)

bmu (best matching unit) (green color)