Gain-scheduled control of nonlinear partial differential equations

The conditions are presented under which a family of linear state-feedback controllers designed for a nonlinear distributed-parameter system can be pieced together to form an overall nonlinear controller. The resulting closed-loop system has the property that its linearizations are equal to the desired linearly-controlled systems. The idea of gain scheduling is considered for systems governed by nonlinear partial differential equations, such as systems involving fluid flow. It is shown that it is possible to apply this technique to finite-dimensional approximations to the original system and to obtain nonlinear feedback laws approximating the ideal controller