Design of Output Feedback Controllers for Nonlinear Systems Using Sum-of-Squares-Programming
نویسنده
چکیده
Zusammenfassung Dieser Beitrag stellt den Entwurf von Ausgangsrückführungen für Systeme mit nicht-polynomialen Nichtlinearitäten mittels SOS-Programmierung vor. Dazu wird eine polynomiale Approximation des Systems durchgeführt und der zugehörige Approximationsfehler bestimmt. Diese Fehlerabschätzung wird im SOS-Programm benutzt, um eine stabilisierende Ausgangsrückführung und eine Lyapunov-Funktion so zu bestimmen, dass ein möglichst großer Einzugsbereich der Ruhelage der Regelung mit dem tatsächlichen System resultiert. Um auf die sich ergebende Regelkreisdynamik Einfluss zu nehmen, wird der lineare Anteil des Reglers vorgegeben, mit dem eine gewünschte Eigenwertverteilung für die Linearisierung des geregelten Systems eingestellt wird. Die für die Stabilisierbarkeit nötigte dynamische Ausgangsrückführung kann dabei durch Erweiterung des Systems um die Dynamik des Reglers auf den Entwurf eines statischen Reglers zurückgeführt werden. Anhand eines einfachen Beispiels wird die vorgestellte Entwurfsmethodik veranschaulicht. Summary This paper presents an output feedback design approach for systems with non-polynomial nonlinearities using SOS-Programming. To this end a polynomial approximation of the system is determinded and the corresponding approximation error is computed. This error is used within the SOS-programm to determine a stabilizing output feedback and a Lyapunov funktion, which yield an as large as possible region of attraction of the equilibrium of the closed-loop original system. In order to influence the dynamics of the resulting closed-loop system, the linear part of the control law is assigned, which is used to assign desired eigenvalues to the linearization of the closed-loop system. If a dynamic output feedback is required for stabilization, the design method can be rewritten as a static output feedback desgin by adding the dynamic of the controller to the system description. A simple example illustrates the presented design approach.
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