A hybrid gradient-LMI algorithm for the synthesis of LPV gain-scheduled controllers

This paper presents an algorithm for solving optimization problems with bilinear matrix inequality (BMI) constraints, which frequently appear in controller synthesis. The algorithm is based on a combination of gradient-based optimization and linear matrix inequalities (LMIs), which makes it fast and enables it to handle a large number of decision variables. Here it is used to synthesize fixed-structure and low-order gain-scheduled controllers for linear parameter varying (LPV) systems, using the idea of quadratic separation. It is known that the synthesis problem based on quadratic separation leads to BMIs. The synthesis technique is applied to design fixed-structure and low-order gain-scheduled controllers for a spark ignition engine, and results are compared with existing approaches to solve BMI constraint optimization problems. It turns out that the proposed algorithm gives solutions where other approaches may fail.