Recently, a new data-driven method for robust control with H_∞ performance has been proposed. This method is based on convex optimization and converges to the optimal performance when the controller order increases. However, for low-order controllers, the performance depends heavily on the choice of some fixed parameters that are used for convexifying the optimization problem. In this paper, several data-driven optimization algorithms are proposed to improve the solution for low-order controllers. A non-convex problem is solved (in a data-driven sense) where the parameters of a fixed-structure low-order controller are optimized; the solution to the problem guarantees the stability of the closed-loop system whilst ensuring robust performance. It is shown that by optimizing all of the controller parameters, the H_∞ performance for low-order controllers can be significantly improved. The simulation examples illustrate how the proposed method can be used to eliminate the sensitivity associated with the fixed parameters and optimize the system performance.
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