Modern tools for control of non-linear systems

In military as well as industrial applications there are complex machines with a dedicated task to perform. Substantial benefits can be drawn from improving the performance and efficiency of these machines, and the modern tools of nonlinear control theory can make this possible in many applications. Regardles of the purpose of the system to be controlled, there are three main ingredients that are needed. A good model of the complete system including uncertanties, a good and accurate measure of the objectives to achieve and a tool for control synthesis and system modeling and analysis. This report presents advances in methods for model order reduction, which is a key ingredient in the modeling phase of controller design for complex systems. Further a number of synthesis methods for stability and tracking, including nonlinear dynamic inversion (NDI), sliding modes and backstepping, are reviewed along with a simple example. A new result on tracking properties for the zero-dynamics of a backstepping controller are also included. A brief introduction to optimisation based control including a problem formulation for open-loop robust control and dynamic games follows. The final chapter presents an example of control law design based on the powerful techniques for block/vector backstepping recently introduced in the literature. Utilizing these techniques it is possible to quickly synthesize a controller with desirable properties for simultaneous control in pitch, yaw and roll which is illustrated for a realistic model of a fighter aircraft.