Double internal loop higher-order recurrent neural network-based adaptive control of the nonlinear dynamical system

• Published in: Soft computing (Berlin, Germany) Vol. 27; no. 22; pp. 17313 - 17331
• Main Author: Kumar, Rajesh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023; Springer Nature B.V
• Subjects: Adaptive control; Adaptive learning; Algorithms; Application of Soft Computing; Artificial Intelligence; Artificial neural networks; Back propagation networks; Complexity; Computational Intelligence; Control; Control theory; Controllers; Dynamical systems; Engineering; Feedback; Feedback loops; Iterative methods; Machine learning; Mathematical Logic and Foundations; Mechatronics; Neural networks; Neurons; Nonlinear control; Nonlinear systems; Parallel processing; Performance enhancement; Recurrent neural networks; Robotics; System theory; Topology; Nonlinear adaptive control; Recurrent neural networks; Adaptive learning rate; Pi-sigma neural network; Higher-order networks
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-023-08061-8

Controlling complex nonlinear dynamical systems using traditional methods has always been a difficult task because the majority of systems seen in nature have intricate nonlinear mathematical relationships. Artificial neural network (ANN) models are a good option for handling such intricate nonlinear systems since they include a number of significant properties like faster learning, adaptation, parallel processing, and nonlinear mapping capabilities. Several recurrent neural networks (RNNs)-based controllers have been suggested in the literature for implementing adaptive control, but the majority of these models have extremely complex topologies and many of them are challenging to train. In this paper, an attempt is made to put forward the RNN model (called as higher-order recurrent neural network (HORNN)) which is based on a higher order Pi-Sigma neural network (PSNN) model and implemented for the indirect adaptive control of the nonlinear dynamical system. The parameters of the proposed controller are tuned using the gradient-descent-based asynchronous back-propagation (BP) method. The proposed controller consists of two additional internal feedback loop layers (denoted by F L 1 and F L 2 ) corresponding to the hidden and the output layer, respectively. The nodes present in F L 1 and F L 2 layers are having weighted connections with the hidden and the output layer neurons, respectively, and these feedback connections enrich the controller with a memory property. The second contribution of the paper is to improve the performance of the learning algorithm which is achieved by incorporating an adaptive learning rate scheme (that ensures the correct setting of the learning rate value in each iteration). Another advantage of the HORNN-based controller is that it is only provided with three inputs irrespective of the dynamics of the plant and only 3 hidden neurons are included in its hidden layer (this reduces the overall structural complexity of the proposed model). The performance of the HORNN-based controller is compared with some of the popular neural networks such as diagonal recurrent neural network (DRNN), Jordan recurrent neural network (JRNN), feed-forward neural network (FFNN), and PSNN. Through simulation experiments, it is observed that the response obtained from the plant under HORNN-based controller is found to be better as compared to responses obtained with other ANN-based controllers. Further, the instantaneous mean square error (IMSE) obtained with HORNN-based controller is quite less and is equal to 0.058 as compared to 0.077, 0.082, 1.74, 13.43, and 1.86 with DRNN, JRNN, PSNN, FFNN, and FFNN (with 30 hidden neurons)-based controllers, respectively.