Learning stabilization of linear unknown unstable systems

The common feature of many theories and methodologies for mutually enhanced plant identification and model-based robust control design is to treat identification and design jointly. The authors propose an effective scheme for finding a stabilizing controller for an unknown and unstable plant with output disturbances. Our idea is to make successive use of the optimal parameter selection (OPS) technique for modelling the plant and the maximally robust control design technique for stabilizing it. We start by constructing an initial model with a limited amount of input-output data in the open loop environment by the OPS technique. Then, we proceed to design a controller which not only stabilizes the model but also achieves the greatest robustness with respect to perturbations around the model in a certain sense. Next, we apply the obtained controller to the plant, and then collect the input-output data of the closed-loop system. It is reasonable to expect that richer accountable data is obtainable in this improved closed-loop environment. This will enable us to use the OPS technique to construct a new model which will contain more information about the plant. This process can go on until a controller is found which stabilizes the plant