Chapter 5 - Semiempirical Neural Network Models of Controlled Dynamical Systems

Abstract

In this chapter we discuss the hybrid, semiempirical (“gray box”) neural network–based modeling approach. Semiempirical models rely on both the theoretical knowledge of the system and the experimental data on its behavior. As evidenced by the results of numerous computational experiments, such models possess high accuracy and computational speed. Also, the semiempirical modeling approach makes it possible to state and solve the identification problem for the characteristics of dynamical systems. That is a problem of great importance, and it is traditionally difficult to solve. These semiempirical ANN-based models possess the required adaptivity feature, just like the pure empirical ones. First, we describe the properties of semiempirical state space continuous time ANN-based models. Then, we outline the stages of the model design procedure and present an illustrative example. We discuss the continuous time counterparts of real-time recurrent learning and backpropagation through time algorithms required for the computation of error function derivatives. We also describe the homotopy continuation training method for semiempirical ANN-based models. Finally, we treat the topic of optimal design of experiments for semiempirical models of controlled dynamical systems.