Weak Interactions Based System Partitioning Using Integer Linear Programming
For control engineers, this provides a systematic partitioning method, but it is incremental as it reformulates an existing problem into ILP.
The paper addresses system partitioning for controller design by minimizing inter-subsystem interactions, formulating it as an integer linear programming problem with search space cuts to ensure controllable subsystems. Two examples demonstrate the methodology.
The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given partitioning, the total magnitude of the interactions between subsystem models is evaluated. Therefore, the partitioning problem seeking for weak interactions can be posed as a minimization problem. Initially, the problem is formulated as a non-linear integer minimization that is then relaxed into a linear integer programming problem. It is shown within this paper that cuts can be applied to the initial search space in order to find the least interacting partitioning; only composed of controllable subsystems. Two examples are given to demonstrate the methodology.