Region of Attraction with Performance Bounds

In this paper we introduce the notion of region of attraction with performance bounds as a useful tool for design and analysis of adaptive control systems. The benefit of using this tool is that ensuring the closed-loop dynamics for the adaptive system within this specific region can guarantee both stability and performance requirements. In this paper, we first define a region of attraction with performance bounds for a nonlinear system. We then compare it with the existing idea of a region of attraction for a nonlinear system with an illustrative example. Next, we demonstrate the usage of this new design and analysis tool with two aircraft adaptive control examples. The first example deals with the analysis of an adaptive controller for the roll-rate dynamics of an aircraft. We show that the region of attraction with performance bounds can be estimated by solving a Sum-of-Squares (SOS) relaxation of the problem which provides an efficient computation technique. The second example deals with designing an adaptive controller for the unstable short-period dynamics of an aircraft. In this example, the adaptive controller is augmented on a baseline dynamic inversion baseline control law. We demonstrate that we can use this tool to perform adaptive control design tradeoffs in an efficient manner.