Domain of attraction for optimization of data-based H2 control performance criterion

Data-based controller design methods tune control parameters directly from a single set of data without a process model. Since nonlinear optimization problems need to be solved in these methods, the convergence property is a signi cant issue. The analysis using a domain of attraction (DOA) is an effective approach providing the condition that a gradient descent converges to the global minimum from a set of initial parameters. However, the analytical results of DOA are not applicable to the data-based controller design because the cost function discussed in the prior research consists of a process model. The present work aims to derive a DOA for the H₂ performance criterion of the sensitivity function derived from input and output data. The analytical results show that a gradient descent algorithm can converge to the global minimum if the ratio of the desired controller transfer function to the controller transfer function satis es the strictly positive real condition. In addition, the obtained results are illustrated through a numerical simulation.