Control Reconfiguration of Cyber-physical Systems for Improved Performance via Reverse-engineering and Accelerated First-order Algorithms

This paper presents a control reconfiguration approach to improve the performance of a certain class of dynamical systems. Motivated by recent research on re-engineering cyber-physical systems, we propose a three-step control retrofit procedure. Firstly, we reverse-engineer a dynamical system as a gradient descent algorithm to solve an unconstrained convex optimization problem. Secondly, we apply a heavy ball method or an accelerated gradient descent algorithm with constant coefficients to solve this optimization problem. Finally, by com-paring the original and accelerated dynamics, we obtain the implementation of the redesigned part (i.e., the extra dynamics). As a result, the convergence rate/speed of the given system can be improved, while the system structure remains. Three practical applications, including consensus in multi-agent systems, Internet congestion control and temperature control in buildings, show the effectiveness of the proposed redesign approach.