Linear Parameter-Varying Systems - an approach to gain scheduling

Abstract: In recent years the interest for gain scheduling methods has increased. Gain scheduling is a collection of methods that try to tackle the challenging problem of nonlinear control in a divide and conquer manner. The use of local linear system theory to obtain a non-local controller is the fundament of the gain scheduling methods. However, the local descriptions of the nonlinear system cannot capture the non-local behavior. Hence, gain scheduling methods may not result in a controller that meets the specifications of the feedback system. Introducing Linear Parameter-Varying (LPV) systems as an intermediate system description in the controller synthesis enables a systematic way of obtaining the nonlinear controller in a linear-like fashion.

In this thesis, LPV systems are investigated in a gain scheduling context. The non-trivial procedure of describing a nonlinear system in the LPV form is investigated and different approaches to obtain an LPV system that is suitable for synthesis purposes are presented.

Computational aspects, in terms of parameterized linear matrix inequalities, of LPV controller synthesis in an L2 gain framework is investigated. A procedure to obtain a fixed order LPV controller is presented. Finally, it is shown that a controller obtained by LPV based gain scheduling gives the expected nonlinear non-local behavior of the feedback system in a domain that is readily determined from the LPV synthesis.

The consequence of the results in this thesis is that the obtained controller in closed loop meets certain specifications of the closed loop system. The synthesis can be done in a computationally tractable and systematic way. Hence, the LPV based gain scheduling approach is a worthy competitor to other controller synthesis methods for nonlinear systems.