Necessary and sufficient conditions for the design of cooperative shared control

In a shared control system humans and machines cooperatively interact. From the control theoretic point of view this can be seen as a system which is controlled by several controllers that are either formed by a human or by a machine. Since all controllers influence the system they affect each other. However, the human parts are given and cannot be changed. Therefore, the question is how to design the non-human controller systematically stable and without experiments. In this paper a design concept for these controllers is proposed which is based on game theoretic modeling. We show that adding a controller to the overall system has to lead to a Nash equilibrium. We further show that remaining degrees of freedom may then be used to optimize the designed controller with respect to a certain global objective function that specifies the demands of the system designers. Based on this idea necessary and sufficient conditions for cooperative shared design are stated. Practical approaches to solve the design problem are presented for real world problems. An example shows the applicability of the concept.