Page 17 - Neural Network Modeling and Identification of Dynamical Systems

NEURAL NETWORK MODELING AND IDENTIFICATION OF DYNAMICAL SYSTEMS 5
tation of a nonlinear model of some dynamical box)-type ANN models. Also, synthesis of neu-
system motion with high efficiency. Using such rocontrollers is carried out.
representation, we synthesize a neural controller In Chapter 5 we discuss the hybrid, semiem-
that solves the problem of adjusting the dynamic pirical (“gray box”) neural network–based mod-
properties of the controlled object (maneuver- eling approach. Semiempirical models rely on
able aircraft). The next problem we solve in both the theoretical knowledge of the system
this chapter relates to designing control laws for and the experimental data on its behavior. As
multimode objects, in particular for airplanes. evidenced by the results of numerous compu-
We consider here the concept of an ensemble tational experiments, such models possess high
of neural controllers (ENC) concerning the con- accuracy and computational speed. Also, the
trol problem for a multimode dynamical system semiempirical modeling approach makes it pos-
(MDS) as well as the problem of optimal synthe- sible to state and solve the identification prob-
sis for the ENC. lem for the characteristics of dynamical sys-
Chapter 4 deals with black box neural net- tems. That is a problem of great importance,
work modeling of nonlinear dynamical systems and it is traditionally difficult to solve. These
for the example of aircraft controlled motion. semiempirical ANN-based models possess the
First of all, we consider the design process required adaptivity feature, just like the pure
for ANN empirical dynamical system models, empirical ones. First, we describe the properties
which belong to the family of black box models. of semiempirical state space continuous time
The basic types of such models are described, ANN-based models. Then, we outline the stages
and approaches to taking into account disturb- of the model design procedure and present an
ing actions on the dynamical system are ana- illustrative example. We discuss the continuous
lyzed. Then, we construct the ANN model of time counterparts of Real-Time Recurrent Learn-
the aircraft motion based on a multilayer neu- ing (RTRL) and backpropagation through time
ral network. As a baseline model, a multilay- (BPTT) algorithms required for the computation
ered neural network with feedbacks and delay of error function derivatives. We also describe
lines is considered, in particular, NARX- and the homotopy continuation training method for
NARMAX-type models. The training of such semiempirical ANN-based models. Finally, we
an ANN model in batch mode and in real-time treat the topic of optimal design of experiments
mode is described. Then, the performance of the for semiempirical models of controlled dynami-
obtained ANN model of the aircraft motion is cal systems.
evaluated for an example problem of the longi- Chapter 6 presents the simulation results that
tudinal short-period aircraft motion modeling. show how efficient the semiempirical approach
The performance evaluation of the model is car- is to the simulation of controlled dynamical sys-
ried out using computational experiments. One tems and to the solution of problems of identify-
of the most important applications of dynami- ing their characteristics. First, the simpler task of
cal models is related to the problem of adaptive modeling the longitudinal short-period motion
control for such systems. We consider the so- of a maneuverable aircraft is considered. After
lution to the problem of adaptive fault-tolerant that, the problem of modeling the total angu-
control for nonlinear dynamical systems oper- lar motion of a maneuverable aircraft is solved,
ating under uncertainty conditions to demon- as well as the ANN identification problem of
strate the potential capabilities of ANN models aerodynamic characteristics for it (lift and lateral
in this area. We apply both the model reference force coefficients, roll, yaw, and pitch moment
adaptive control (MRAC) and model predictive coefficients) obtained as nonlinear functions of
control (MPC) methods using empirical (black several variables. Then, another identification