Neural Networks in Multidimensional Domains Fundamentals and New Trends in Modelling and Control

In this monograph, new structures of neural networks in multidimensional domains are introduced. These architectures are a generalization of the Multi-layer Perceptron (MLP) in Complex, Vectorial and Hypercomplex algebra. The approximation capabilities of these networks and their learning algorithms are discussed in a multidimensional context. The work includes the theoretical basis to address the properties of such structures and the advantages introduced in system modelling, function approximation and control. Some applications, referring to attractive themes in system engineering and a MATLAB software tool, are also reported. The appropriate background for this text is a knowledge of neural networks fundamentals. The manuscript is intended as a research report, but a great effort has been performed to make the subject comprehensible to graduate students in computer engineering, control engineering, computer sciences and related disciplines.

to MLP neural networks.- Neural networks in complex algebra.- Vectorial neural networks.- Quaternion algebra.- MLP in quaternion algebra.- Chaotic time series prediction with CMLP and HMLP.- Applications of quaternions in robotics.