Privacy Preservation by Local Design in Cooperative Networked Control Systems

Abstract

In this paper, we study the privacy preservation problem in a cooperative networked control system, which has closed-loop dynamics, working for the task of linear quadratic Guassian (LQG) control. The system consists of a user and a server: the user owns the plant to control, while the server provides computation capability, and the user employs the server to compute control inputs for it. To enable the server's computation, the user needs to provide the measurements of the plant states to the server, who then calculates estimates of the states, based on which the control inputs are computed. However, the user regards the states as privacy, and makes an interesting request: the user wants the server to have "incorrect" knowledge of the state estimates rather than the true values. Regarding that, we propose a novel design methodology for the privacy preservation, in which the privacy scheme is locally equipped at the user side not open to the server, which manages to create a deviation in the server's knowledge of the state estimates from the true values. However, this methodology also raises significant challenges: in a closed-loop dynamic system, when the server's seized knowledge is incorrect, the system's behavior becomes complex to analyze; even the stability of the system becomes questionable, as the incorrectness will accumulate through the closed loop as time evolves. In this paper, we succeed in showing that the performance loss in LQG control caused by the proposed privacy scheme is bounded by rigorous mathematical proofs, which convinces the availability of the proposed design methodology. We also propose an associated novel privacy metric and obtain the analytical result on evaluating the privacy performance. Finally, we study the performance trade-off between privacy and control, where the accordingly proposed optimization problems are solved by numerical methods efficiently.