Coding for Decentralized Control System
Mentor:Tracey Ho, Assistant professor of Electrical Engineering and Computer Science, California Institute of Technology
We study error correcting codes for decentralized control systems. Unlike existing work which considers coding for control of an unstable plant, we consider coding for cost minimization in networks of stable interacting plants and find that different codes are needed. We consider a two-player model where each player has a plant and a controller. The dynamics of each plant affects the other plant in D time steps, which is termed the “dynamics delay” of the system. In addition, the players communicate their states to the other player’s controller after a d steps communication delay. The optimal control problem has been solved when the communication is assumed to be lossless and one step delayed. In our work, we model that communication link between the two players to be packet erasure link. It is found that for systems with one step dynamics delay, coding seems unnecessary. Whereas, in general if there is a D (>1) steps dynamics delay between the two plants, the success transmission of the state x(t-D+1) to the other player’s controller is critical for ensuring a near-optimal performance of the overall system. For such system, real time streaming code previous studied by Derek et al. can be applied directly. Further generalization shows that for higher order system where multiple states affect the dynamics of the neighboring node, multiple deadline streaming code is necessary. Here, we propose a novel construction of such multiple deadline streaming code and show its optimality.