Sequential convex optimisation with adaptive feasible sets for fixed-order dynamic output feedback control

This paper addresses a generic method for optimisation problems subject to bilinear matrix inequalities (BMIs), with application to dynamic output feedback (DOF) synthesis. Such problems are inherently nonconvex and NP-hard. To tackle this challenge, we develop an inner-approximation strategy that iteratively searches for a convex surrogate within a family of alternative constraints. The proposed algorithm features adaptive feasible sets and is equipped with a convergence guarantee. In a generic algorithmic framework to solve fixed-order DOF control problems for linear systems, we formulate an iterative procedure for calculating the control law. Numerical experiments on benchmarks from the COMPleib library demonstrate the effectiveness and superiority of the proposed approach.