Linear, Time-varying Approximations to Nonlinear Dynamical Systems: with Applications in Control and Optimization

✍ Scribed by María Tomás-Rodríguez, Stephen P. Banks (auth.)

• Publisher: Springer-Verlag London
• Year: 2010
• Tongue: English
• Leaves: 302
• Series: Lecture Notes in Control and Information Sciences 411
• Edition: 1
• Category: Library

✦ Synopsis

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems.

Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

✦ Table of Contents

Front Matter....Pages -
Introduction to Nonlinear Systems....Pages 1-10
Linear Approximations to Nonlinear Dynamical Systems....Pages 11-28
The Structure and Stability of Linear, Time-varying Systems....Pages 29-60
General Spectral Theory of Nonlinear Systems....Pages 61-74
Spectral Assignment in Linear, Time-varying Systems....Pages 75-100
Optimal Control....Pages 101-121
Sliding Mode Control for Nonlinear Systems....Pages 123-139
Fixed Point Theory and Induction....Pages 141-150
Nonlinear Partial Differential Equations....Pages 151-167
Lie Algebraic Methods....Pages 169-194
Global Analysis on Manifolds....Pages 195-217
Summary, Conclusions and Prospects for Development....Pages 219-228
Back Matter....Pages -

✦ Subjects

Control;Optimization;Statistical Physics, Dynamical Systems and Complexity;Systems Theory, Control