Gain-Scheduled Controller Design

Doctoral thesis, 2015

This thesis is devoted to controller synthesis, i.e. to finding a systematic procedure to determine the optimal (sub-optimal) controller parameters which guarantees the closed-loop stability and guaranteed cost for uncertain nonlinear systems with considering input/output constraints, all this without on-line optimization. The controller in this thesis is given in a feedback structure that is, the controller has information about the system and uses this information to influence the system. In this thesis the linear parameter-varying based gain scheduling is investigated. The nonlinear system is transformed to a linear parameter-varying system, which is used to design a controller, i.e. a gain-scheduled controller with consideration of the objectives on the system. The gain-scheduled controller synthesis in this thesis is based on the Lyapunov theory of stability as well as on the Bellman-Lyapunov function. Several forms of parameter dependent/quadratic Lyapunov functions are presented and tested. To achieve performance quality a quadratic cost function and its modifications known from LQ theory are used. In this thesis one can find also an application of gain scheduling in switched and in model predictive control with consideration of input/output constraints. The main results for controller synthesis are in the form of bilinear matrix inequalities (BMI) and/or linear matrix inequalities (LMI). For controller synthesis one can use a free and open source BMI solver PenLab or LMI solvers LMILab or SeDuMi. The synthesis can be done in a computationally tractable and systematic way, therefore the linear parameter-varying based gain scheduling approach presented in this thesis is a worthy competitor to other controller synthesis methods for nonlinear systems.