Elman Neural Networks In Model Predictive Control

Abstract

The goal of this paper is to present interesting way how to model and predict nonlinear systems using recurrent neural network. This type of artificial neural networks is underestimated and marginalized. Nevertheless, it offers superior modelling features at reasonable computational costs. This contribution is focused on Elman Neural Network, two-layered recurrent neural network. The abilities of this network are presented in the nonlinear system control. The task of the controller is to control the liquid level in the second of two interconnected cylindrical tanks. The mathematical model of the realtime system was derived in order to test predictor and consequently the controller in Matlab/Simulink simulations. INTRODUCTION Model predictive control (MPC) (Camacho and Bordons 2007) is a very popular concept for the development and tuning of nonlinear controllers in the presence of input, output or state constraints. Many predictive control techniques based on MPC that use artificial neural network (ANN) as a predictor are established on multilayer feed-forward neural networks (Hagan et al. 2002), (Kanjilal 1995). In spite the multilayer feedforward neural networks (MFFNNs) have many advantages such as simple design and scalability, they have also many drawbacks such as long training times and choice of an appropriate learning stop time (the over-learning versus the early stopping problem). However, there is quite a number of types ANNs suitable for the modelling and prediction, for instance adaptive linear networks, radial basis function networks and recurrent networks (Liu 2001), (Meszaros et al. 1999), (Koker 2006). This paper is divided as follows: After short introduction to the recurrent neural networks, the used model predictive controller is explained. Then the model of the real time system is derived. After that the identification of the predictor (training of the artificial neural network) is described. When the identification is finished, the paper focuses on the model predictive control and evaluation of results. The contribution is finished by some concluding remarks. RECURRENT NEURAL NETWORKS Recurrent neural networks (sometimes are these networks called feedback neural networks) can be distinguished from feed-forward neural networks in that they have a loopback connection (Figure 1). In its most general form recurrent network consist of a set of processing units, while the output of each unit is fed as input to all other units including the same unit. With each link connecting any two units, a weight is associated which determines the amount of output a unit feeds as input to the other unit (Yegnanarayana 2005). Figure 1: Example of Recurrent Neural Network Recurrent neural networks have superior temporal and spatial behaviours, such as stable and unstable fixed points and limit cycles, and chaotic behaviours. These behaviours can be utilized to model certain cognitive functions, such as associative memory, unsupervised learning, self-organizing maps, and temporal reasoning (He 1999). Elman Neural Networks One of the most known recurrent neural networks is Elman neural network (Elman 1990). Typical Elman network has one hidden layer with delayed feedback. The Elman neural network is capable of providing the standard state-space representation for dynamic systems. This is the reason why this network architecture is utilized as a recurrent neural equalizer. Proceedings 23rd European Conference on Modelling and Simulation ©ECMS Javier Otamendi, Andrzej Bargiela, Jose Luis Montes, Luis Miguel Doncel Pedrera (Editors) ISBN: 978-0-9553018-8-9 / ISBN: 978-0-9553018-9-6 (CD) Generally, this network is considered as a special kind feed-forward network, including additional memory neurons and local feedback (Koker 2006). Typical structure of Elman neural network is depicted in fig. 2. Figure 2: Elman Neural Network MODEL PREDICTIVE CONTROL There are various approaches to predictive control by artificial neural networks. Generally we can say that these methods use ANN as the plant model in order to get its output predictions. The most used approach is model predictive control (Camacho and Bordons 1995). MPC is a broad control strategy applicable to both linear and nonlinear processes. The main idea of MPC algorithms is to use a dynamical model of process to predict the effect of future control actions on the output of the process. Hence, the controller calculates the control input that will optimize the performance criterion over a specified future time horizon: