Nonlinear missile autopilot design using a density function-based sum-of-squares optimization approach

This paper presents a procedure of a Sum-Of-Squares (SOS) based autopilot design for a Skid-To-Turn (STT) missile. In particular, we consider a nonlinear short period mode in the pitch dynamic model of a SRAAM (Short-Range Air-to-Air Missile). A nonlinear state-feedback controller is designed using SOS Optimization approach, taking advantage of its capability of transforming a control design problem into a convex optimization problem. The dynamic model for autopilot design is represented as polynomial equations through the approximation of aerodynamic coefficients. Then, appropriate density functions, based on the dual Lyapunov theorem, are introduced to formulate the nonlinear control design as a convex program. The performance of the proposed method is verified via numerical simulations, including the case with uncertainty in the aerodynamic coefficients.