Distributed Control of a System of Systems: An Alternating Direction Method of Multipliers Approach

In a system of systems, a system can be modelled as a set of interacting subsystems. When each subsystem can be separately controlled, a distributed algorithm can be applied to manage the control. In this work, we propose a distributed approach, the Alternating Direction Method of Multipliers (ADMM), based on a distributed Linear Quadratic Regulator (LQR) approach to manage the achievement of a common goal cooperatively. The proposed approach can work with different agents with a limited observation of the system of systems state. The method is demonstrated on a natural system including four interconnected water tanks (quad tank system) whose level can be controlled by two pumps. The results show the behaviour of the proposed algorithm when the tanks have to reach a constant set point and when they must agree on a time-varying set point.