Iterative Data-Driven Control for Closed Loop with Two Unknown Controllers

Iterative idea is combined with data-driven control and is used to design the feedforward controller and feedback controller simultaneously. Consider one closed loop system with two controllers, the classical model-based control holds on the condition of known plant. To alleviate the modeling process for plant, data-driven control is applied to design the two controllers. After these two controllers are parametrized by two unknown parameter vectors, the iterative idea is introduced to identify these two parameter vectors. Furthermore, for more general case of controllers, the closed relations between controllers and expected transfer functions are derived. Then, the iterative idea is also introduced to achieve the controller design. To be of benefit for latter stability analysis, some equities are derived for output-input sensitivity functions with three kinds of disturbances. Generally, after formulating the problem of the controller design as one model-matching problem, the purpose of this paper is threefold. First, we derive that, in case of two parametrized controllers, the iterative idea is performed to identify these two unknown parameter vectors, even when parameters converge to their true values. Second, we show how to design the two controllers iteratively for more general forms and find the closed relations between these controllers and expected closed loop transfer functions. Third, we provide some heuristic considerations on output-input sensitivity functions, which are of benefit for our stability analysis on data-driven control. Finally, one example is given to show the feasibility of our proposed theories.