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The subject of this book is model abstraction of dynamical systems.
The p- mary goal of the work embodied in this book is to design a
controller for the mobile robotic car using abstraction.
Abstraction provides a means to rep- sent the dynamics of a system
using a simpler model while retaining important characteristics of
the original system. A second goal of this work is to study the
propagation of uncertain initial conditions in the framework of
abstraction. The summation of this work is presented in this book.
It includes the following: * An overview of the history and current
research in mobile robotic control design. * A mathematical review
that provides the tools used in this research area. * The
development of the robotic car model and both controllers used in
the new control design. * A review of abstraction and an extension
of these ideas into new system relationship characterizations
called traceability and -traceability. * A framework for designing
controllers based on abstraction. * An open-loop control design
with simulation results. * An investigation of system abstraction
with uncertain initial conditions.
A Practical Approach to Dynamical Systems for Engineers takes the
abstract mathematical concepts behind dynamical systems and applies
them to real-world systems, such as a car traveling down the road,
the ripples caused by throwing a pebble into a pond, and a clock
pendulum swinging back and forth. Many relevant topics are covered,
including modeling systems using differential equations, transfer
functions, state-space representation, Hamiltonian systems,
stability and equilibrium, and nonlinear system characteristics
with examples including chaos, bifurcation, and limit cycles. In
addition, MATLAB is used extensively to show how the analysis
methods are applied to the examples. It is assumed readers will
have an understanding of calculus, differential equations, linear
algebra, and an interest in mechanical and electrical dynamical
systems.
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