Page 801 - Mechanical Engineers' Handbook (Volume 2)

792 Neural Networks in Feedback Control Systems

1 INTRODUCTION
Dynamical systems are ubiquitous in nature and include naturally occurring systems such as
the cell and more complex biological organisms, the interactions of populations, and so on,
as well as man-made systems such as aircraft, satellites, and interacting global economies.
1
Von Bertalanffy were among the first to provide a modern theory of systems at the beginning
of the century. Systems are characterized as having outputs that can be measured, inputs that
can be manipulated, and internal dynamics. Feedback control involves computing suitable
control inputs, based on the difference between observed and desired behavior, for a dynam-
ical system such that the observed behavior coincides with a desired behavior prescribed by
the user. All biological systems are based on feedback for survival, with even the simplest
of cells using chemical diffusion based on feedback to create a potential difference across
the membrane to maintain its homeostasis, or required equilibrium condition for survival.
Volterra was the first to show that feedback is responsible for the balance of two populations
of fish in a pond, and Darwin showed that feedback over extended time periods provides
the subtle pressures that cause the evolution of species.
There is a large and well-established body of design and analysis techniques for feed-
back control systems which has been responsible for successes in the industrial revolution,
ship and aircraft design, and the space age. Design approaches include classical design
methods for linear systems, multivariable control, nonlinear control, optimal control, robust
control, H control, adaptive control, and others. Many systems one desires to control have

unknown dynamics, modeling errors, and various sorts of disturbances, uncertainties, and
noise. This, coupled with the increasing complexity of today’s dynamical systems, creates a
need for advanced control design techniques that overcome limitations on traditional feed-
back control techniques.
In recent years, there has been a great deal of effort to design feedback control systems
that mimic the functions of living biological systems. There has been great interest recently
in ‘‘universal model-free controllers’’ that do not need a mathematical model of the controlled
plant but mimic the functions of biological processes to learn about the systems they are
controlling online, so that performance improves automatically. Techniques include fuzzy
logic control, which mimics linguistic and reasoning functions, and artificial neural networks
(NNs), which are based on biological neuronal structures of interconnected nodes, as shown
in Fig. 1. By now, the theory and applications of these nonlinear network structures in
feedback control have been well documented. It is generally understood that NNs provide
an elegant extension of adaptive control techniques to nonlinearly parameterized learning
systems.
This chapter shows how NNs fulfill the promise of providing model-free learning con-
trollers for a class of nonlinear systems, in the sense that a structural or parameterized model
of the system dynamics is not needed. The control structures discussed are multiloop con-
trollers with NNs in some of the loops and an outer tracking unity-gain feedback loop.
Throughout, there are repeatable design algorithms and guarantees of system performance,
including both small tracking errors and bounded NN weights. It is shown that as uncertainty
about the controlled system increases or as one desires to consider human user inputs at
higher levels of abstraction, the NN controllers acquire more and more structure, eventually
acquiring a hierarchical structure that resembles some of the elegant architectures proposed
by computer science engineers using high-level design approaches based on cognitive lin-
guistics, reinforcement learning, psychological theories, adaptive critics, or optimal dynamic
programming techniques.
Many researchers have contributed to the development of a firm foundation for analysis
and design of NNs in control system applications. See Section 11 on historical development
and further study.