A data-driven approach to robust control of multivariable systems by convex optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parameterized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like H2, H∞ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex–concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimum or a saddle point in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controller design methods based on non-smooth optimization via multiple simulation examples.