Optimized distributed control and network topology design for interconnected systems

This paper considers optimized network topology design and distributed control for linear discrete-time systems consisting of subsystems interconnected through states, inputs, and a cost function. By using a distributed control law, which makes use of the communicated states of other subsystems, closed-loop performance is increased at the expense of communication costs. This raises the question of how to find a topology and associated distributed control law with optimal trade-off between communication costs and closed-loop performance. As an answer to this question, we propose an approach to simultaneous optimization of network topology and control law with respect to a cost function which combines a quadratic performance criterion with costs associated to the presence of communication links. The problem is formulated as mixed-integer semi-definite problem (MISDP) where the discrete optimization of the network topology subject to communication constraints and embedded subproblems for structured controller synthesis lead to an upper bound for the combined cost. An example is used to illustrate the method.