Chapter 3 - Neural Network Black Box Approach to the Modeling and Control of Dynamical Systems

Abstract

In this chapter, we deal with the neural network black box approach to solving problems associated with dynamical systems. We discuss two main strategies to the representation (description) of dynamical systems: state space representations and input–output representations. We consider the ANN-based approach to modeling and identification of dynamical systems. The most natural and efficient approach to implementing models and controlling dynamical systems is based on using recurrent neural networks. We discuss this approach in the next chapter. However, dynamic networks are complicated to learn. For this reason, it is advisable, in situations where possible, to use feedforward networks that are simpler regarding their learning processes. There are two situations when feedforward networks can be used for modeling dynamical systems. In the first one, we solve the problem of modeling some uncontrolled dynamical system, which implements the trajectory depending only on the initial conditions (and possibly disturbances acting on the system). For a single variant of the initial conditions, the solution of the problem will be a trajectory described by some function which is nonlinear in the general case. This trajectory we can represent using some feedforward network. The second situation is related to the block-oriented approach to system modeling. With this approach, the dynamical system is represented as a set of interrelated and interacting blocks. Some of these blocks will represent the realization of some functions that are nonlinear in the general case. These nonlinear functions we can realize in various ways, including in the form of a feedforward neural network. Then we attempt to show in this chapter that using ANN technology we can solve the problem of appropriate representation (approximation) of a nonlinear model of some dynamical system (aircraft) motion with high efficiency. Using such approximation, we can synthesize a neural controller that solves the problem of adjusting the dynamic properties of this controlled object. The next problem we solve in this chapter relates to designing control laws for multimode objects, in particular for airplanes. We consider here the concept of an ensemble of neural controllers (ENC) concerning the control problem for a multimode dynamical system (MDS) which is, for example, some aircraft. We need to synthesize an optimal ENC for the MDS. To do this, we first create a model of such a system, and then we consider the construction of a neurocontroller for a single-mode dynamical system. On this basis, an ENC is then formed optimally to control the MDS.