Feedback control : systems with higher unknown relative degree, input constraints and positivity
The thesis deals with the control of m-input, m-output systems with unknown but bounded relative degree and Volterra-Stieltjes systems. The two control strategies are: adaptive high-gain output derivative feedback and funnel control. The aim is the development of feedback controllers which achieves output regulation without system identification. Particularly systems with higher relative degree are considered. Firstly, a universal adaptive lambda-tracking controller is designed which achieves a prespecified control objective and tracks any system with known relative degree. This controller is extend to systems with unknown relative degree but an upper bound is known. Secondly, the well known concept of funnel control for relative degree one systems achieves in presence of input saturation the control objectives of funnel control. The presence of explicit input constraints is a distinguished feature of this thesis. The results for funnel control will be generalized to systems with relative degree two and input constraints. This new funnel controller is robust for systems of unknown relative degree one or two. Finally, Volterra-Stieltjes systems are considered with regard to positivity, various stability concepts, zero dynamics and funnel control. These results are exploited to generalize funnel controller to Volterra-Stieltjes systems. Positivity of the closed-loop system is guaranteed, input constraints are possible and non-negativity of the input can be guaranteed.