Robust nonlinear stability and performance analysis of an F/A-18 aircraft model using sum of squares programming

摘要

In this paper, we develop algorithms for the computational analysis of stability and robust performance properties of nonlinear models governed by polynomial differential equations in quasi-Linear Parameter Varying form subject to parametric uncertainty. The methods presented use the sum of squares decomposition and ideas from real algebraic geometry to represent polynomial non-negativity over closed sets to compute various system properties such as L2 gain, regions of attraction, reachable sets and nonlinear Hankel norm approximations. The methods we present are then illustrated on a nonlinear model of an F/A-18 aircraft short-period dynamics subject to uncertainty in the aerodynamic coefficients.