Mixed Fuzzy/Boundary Control Design for Nonlinear Coupled Systems of ODE and Boundary-Disturbed Uncertain Beam

This paper addresses a mixed fuzzy/boundary control problem of a class of nonlinear coupled systems described by ordinary differential equation (ODE) and boundary-disturbed uncertain beam equation. The control scheme consists of an ODE-state feedback fuzzy controller for the ODE system and an antidisturbance robust boundary controller for the boundary-disturbed uncertain beam. The boundary controller includes a linear feedback controller for the beam stabilization via boundary measurements, a nonlinear compensator with adaptive bounding, and a disturbance observer based compensator for canceling the effects of the uncertain nonlinearity and the boundary disturbance of the beam. The mixed control design is developed in terms of space dependent bilinear matrix inequalities (SDBMIs) to guarantee the closed-loop input-to-state practical stability. Meanwhile, the closed-loop well-posedness analysis is also given. Furthermore, a two-step procedure is introduced to solve the SDBMI feasibility problem by the existing linear matrix inequality optimization techniques. Finally, a simulation study on a flexible spacecraft is given to illustrate the effectiveness of the proposed method.