Solving nonconvex optimization problems

It is well known that most analysis and design problems in robust and nonlinear control can be formulated as global optimization problems with polynomial objective functions and constraints. The objective of this article is to show how GloptiPoly can solve challenging nonconvex optimization problems in robust nonlinear control. GloptiPoly is a general-purpose software with a user-friendly interface. First, we describe several nonconvex optimization problems arising in control system analysis and design. These problems involve multivariable polynomial objective functions and constraints. We then review the theoretical background behind GloptiPoly. Next, an example is presented to illustrate the successive linear matrix inequality relaxations and general features of the GloptiPoly software. Finally, we apply GloptiPoly to several control-related problems.