Data-driven optimal output regulation for unknown linear discrete-time systems based on parameterization approach

The output regulation problem has been studied based on a parameterization approach. Different from existing literature, the proposed method does not rely on prior knowledge of the system dynamics. Instead, it leverages state and input data to address the absence of information regarding unmodeled dynamics. Firstly, the output regulation problem is transformed into a stabilization problem by using coordination transformation. The feedback control gain is computed directly by solving an optimization problem using input and state data. The feedforward control gain is obtained by using data-based solutions of regulator equations. Secondly, the design of a dynamic feedback controller is also explored within the framework of a data-driven strategy. Thirdly, two algorithms corresponding to the optimal and dynamic data-driven output regulation problems are developed to implement the proposed data-driven method. Finally, a simulation example is carried out to illustrate the effectiveness of the developed data-driven approach.