Page 8 - Neural Network Modeling and Identification of Dynamical Systems

x PREFACE

Chapter 2 is about the ANN approach to model and control law for this motion. As an
the modeling and control of dynamical sys- example, the problem of modeling a controlled
tems. The classes of ANN models for dynamical longitudinal angular motion of an aircraft is con-
systems are considered in this chapter, includ- sidered. The corresponding motion models for
ing static (feedforward) networks and dynamic aircraft of various classes are obtained for this
(feedback) networks. Possible ways to imple- problem, and their performance is evaluated.
ment the three main elements of the process of These models are then used to form adaptive
forming ANN models are identified: (1) the gen- control systems such as model reference adap-
eration of a potentially rich class of models that tive control (MRAC) and model predictive con-
contains the ANN model being created as an el- trol (MPC), for which a set of applied problems
ement (class instance); (2) obtaining an informa- has been solved. The results obtained for these
tive data set required for the structural and para- tasks allow us to estimate the potentialities of
metric adjustment of the generated ANN model; the ANN simulation for the considered range of
(3) building learning algorithms that carry out
problems. It is shown that in some cases the ca-
structural adjustments and parametric tuning of
pabilities of this class of models are insufficient
the ANN model being formed. In addition, the
when solving problems of modeling controlled
issues of ensuring the adaptability of ANN mod- motion of an aircraft. As a consequence, an ex-
els are considered, which are among the most tension of this class of models is required, which
important from the point of view of solving the
is discussed in Chapters 5 and 6.
problem of aircraft robotization.
Chapter 5 proposes a variant of ANN mod-
In Chapter 3 we study the problem of mod- eling, which expands the possibilities of tradi-
eling the controlled motion of dynamical sys-
tems, an aircraft in particular, using the tradi- tional dynamic ANN models by embedding into
tional ANN modeling tools, in which the model these models the available theoretical knowl-
is based only on experimental data on the be- edge about the object of modeling. The result-
havior of the simulation object, i.e., it is purely ing combined ANN models are called semiem-
empirical (“black box” model). We discuss two pirical (“gray box”) models. The processes of
main strategies to the representation of dynam- formation of such models and the implemen-
ical systems. These are state space representa- tation of the main elements of these processes
tions and input-output representations. We con- are considered. We illustrate their specificity us-
sider the problem of modeling and identification ing a demo example of a dynamical system. The
of dynamic systems, as well as the capabilities of same example, in combination with its sophisti-
feedforward networks and recurrent networks cated variants, is used for the initial experimen-
to solve this problem. Traditional (black box) tal evaluation of the possibilities of semiempir-
networks are used to solve control problems us- ical ANN modeling of controlled dynamic sys-
ing the simple problem of adjusting the dynamic tems. Also we describe in this chapter the prop-
properties of an aircraft as an example. The ex- erties of semiempirical state-space continuous
tension of this approach is the formation of an time ANN-based models. Then, we discuss the
optimal ensemble of neurocontrollers for multi- continuous time counterparts of Real-Time Re-
mode dynamical system. current Learning (RTRL) and backpropagation
Chapter 4 gives examples of solving prob- through time (BPTT) algorithms required for
lems of motion modeling and control based on the computation of error function derivatives.
traditional-type ANN black box models. The We also provide a description of the homotopy
ANN architecture of the NARX type is used, continuation training method for semiempirical
which allows to build both the aircraft motion ANN-based models. Finally, we treat the topic of