An improved sum‐of‐squares based approach to fuzzy tracking control design of nonlinear systems

Abstract

AbstractIn this paper, using a more general Lyapunov function, less conservative sum‐of‐squares (SOS) stability conditions for polynomial‐fuzzy‐model‐based tracking control systems are derived. In tracking control problems the objective is to drive the system states of a nonlinear plant to follow the system states of a given reference model. A state feedback polynomial fuzzy controller is employed to achieve this goal. The tracking control design is formulated as an SOS optimization problem. Here, unlike previous SOS‐based tracking control approaches, a full‐state‐dependent Lyapunov matrix is used, which reduces the conservatism of the stability criteria. Furthermore, the SOS conditions are derived to guarantee the system stability subject to a given H∞ performance. The proposed method is applied to the pitch‐axis autopilot design problem of a high‐agile tail‐controlled pursuit and another numerical example to demonstrate the effectiveness and benefits of the proposed method.