A levenberg-marquardt learning applied for recurrent neural identification and control of a wastewater treatment bioprocess

Abstract

The paper proposed a new recurrent neural network (RNN) model for systems identification and states estimation of nonlinear plants. The proposed RNN identifier is implemented in direct and indirect adaptive control schemes, incorporating a noise rejecting plant output filter and recurrent neural or linear-sliding mode controllers. For sake of comparison, the RNN model is learned both by the backpropagation and by the recursive Levenberg-Marquardt (L-M) learning algorithm. The estimated states and parameters of the RNN model are used for direct and indirect adaptive trajectory tracking control. The proposed direct and indirect schemes are applied for real-time control of wastewater treatment bioprocess, where a good, convergence, noise filtering, and low mean squared error of reference tracking is achieved for both learning algorithms, with priority of the L-M one. C 2009 Wiley Periodicals, Inc.

Centralized Distributed Parameter Bioprocess Identification and I-Term Control Using Recurrent Neural Network Model

“…The reduced plant model (8)- (16), could be used as unknown plant model which generate input/output process data for centralized adaptive neural identification and control system design, based on the concepts, given in (Baruch et al, 2008;Baruch & Mariaca-Gaspar, 2009). …”

“…The stability of the RTNN model is assured by the activation functions (-1, 1) bounds and by the local stability weight bound condition, given by (19). Below it is given a theorem of RTNN stability which represented an extended version of Nava's theorem, (Baruch et al, 2008;Baruch & MariacaGaspar, 2009;Baruch & Mariaca-Gaspar, 2010).…”

“…The multilayer feedforward NN realizing a NARMA model for systems identification has the inconvenience that it is sequential in nature and require input and feedback tap-delays for its realization. In (Baruch et al, 2002;Baruch et al, 2004;Baruch et al, 2005a;Baruch et al, 2005b;Baruch et al, 2007a;Baruch et al, 2007b;Baruch et al, 2008;Baruch & Mariaca-Gaspar, 2009;Baruch & Mariaca-Gaspar, 2010), a new completelly parallel canonical Recurrent Trainable NN (RTNN) architecture, and a dynamic BP learning algorithm has been applied for systems identification and control of nonlinear plants with equal input/output dimensions, obtaining good results. The RTNN do not need the use of tap delays and has a minimum number of weights due to its Jordan canonical structure.…”

“…Furthermore the mathematical model description of the plant help us to understand the work and the meaning of all process variables of this complex biotechnological plant. Here the plant identification by means of RTNN BP learning will be changed by the RTNN Levenberg Marquardt (L-M) second order learning, (Baruch et al, 2009). This distributed nonlinear parameter plant, described by ODE, has excessive high-dimensional measurements which means that the plant output dimension is greater than the plant control input one (rectangular system), requiring to use learning by data fusion technique and special reference choice.…”

Distributed Parameter Bioprocess Plant Identification and I-Term Control Using Decentralized Fuzzy-Neural Multi-Models

“…The general recursive L-M algorithm of learning, (Baruch & Mariaca-Gaspar, 2009) is given by the following equations:…”