In 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.
This paper investigates the suboptimal control design for polynomial timevarying systems. It is known that the solution to this problem relies on the solution of the Hamilton-Jacobi-Bellman (HJB) equation, which is a nonlinear partial differential equation (PDE). A policy iteration (PI) algorithm is developed to solve the HJB equation. The policy evaluation step of this algorithm consists of a sum-of-squares (SOS) program, which is computationally tractable. This algorithm distinguishes from previously known SOS-based adaptive dynamic programming (ADP) algorithms in that it is developed for time-varying systems. The convergence of the iterative algorithm and the global stability of the closed-loop system are proved. At the end, the effectiveness of the proposed algorithm is illustrated through two simulation examples.
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