Practical feedback stabilization of nonlinear control systems and applications
An important and challenging research subject in the field of nonlinear control systems is the impact of input constraints on control performance, which is more realistic in practical problems but much more difficult in mathematical analysis, such as the concepts of controllability, stability, stabilization, domain of attraction, controlled invariance and so on, especially when unstable systems are involved;More precisely, we consider the nonlinear system of the form x = f(x) on a smooth manifold M⊂ Rd together with the family of control-affine systems \dot x=f(x)+[sigma]spi=1mui(t)gi(x) with constrained control range U⊂ Rm. Our specific interest in this dissertation is to introduce the practical feedback control approach which provides a strategy that drives the phase-space trajectory of the nonlinear system arbitrarily close to the unstable limit sets (e.g. fixed points, periodic orbits, etc.) of x = f(x) and stabilizes forever the system in a certain small set;A software based on this theory has been successfully developed by the present author and his colleague Dr. Gerhard Hackl and applied to several models, such as a tunnel diode circuit model, a bacterial respiration model, a chemical reactor model etc.. In particular, we illustrate the numerical simulation of the global feedback controllers and the feedback controlled invariant sets of these examples.