Distributed optimal steady-state control using reverse- and forward-engineering

In this paper, we consider the problem of distributed control for linear network systems to achieve optimal steady-state performance. Motivated by recent research on re-engineering cyber-physical systems, we propose a reverse- and forward-engineering framework which consists of two steps. Firstly, we reverse-engineer a dynamic system as a gradient algorithm to solve an optimization problem. Secondly, we use a forward-engineering approach to systematically design distributed control or modify the existing control. As a result, the system can automatically track the optimal solution of a predefined optimization problem and the control scheme can be implemented in a distributed and closed-loop manner. In order to investigate how general this framework is, we establish necessary and sufficient conditions under which a linear dynamic system can be reverse-engineered as a gradient algorithm to solve an optimization problem. Those conditions are characterized using properties of system matrices and relevant linear matrix inequalities. A practical example regarding frequency control in power systems demonstrates the effectiveness of the proposed framework.