Differential privacy, which has been widely applied in industries, is a privacy mechanism effective in preventing malicious entities from breaching the privacy of an individual participant. It is usually achieved by adding random variables in the data. This article investigates a class of multivariable discrete-time multiagent systems with $\epsilon $ -differential privacy preserved. A novel information-masking mechanism is proposed, in which the information of each state transmitted to different neighbors is obscured by adding independent random noises. Then, the mean-square consensus conditions, and the upper bound and lower bound of the convergence rate are obtained. Moreover, the conditions for the convergence rate reaching its upper bound are established. The results can be applied to the average mean-square consensus. In addition, a necessary and sufficient condition is presented under which agents can preserve the dynamics of agents $\epsilon $ -differentially private at any time instant.

In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a user datagram protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established.

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems, in which both control inputs and observations are randomly lost without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP)-like system; otherwise, it is called a user datagram protocol (UDP)-like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.), and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We characterize the impact of the control/observation p.a.r. and the control input on the estimation performance, and prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound.

This research paper addresses the problem of achieving differentially private average consensus for multiagent systems (MASs) consisting of positive agents. A novel randomized mechanism is introduced that employs nondecaying positive multiplicative truncated Gaussian noises to maintain the positivity and randomness of the state information over time. A time-varying controller is developed to achieve mean-square positive average consensus, and convergence accuracy is evaluated. The proposed mechanism is shown to preserve $(\epsilon,\delta)$ -differential privacy of MASs, and the privacy budget is derived. Numerical examples are provided to illustrate the effectiveness of the proposed controller and privacy mechanism.

For a multiple-channel system with sensor measurement losses, if the loss of sensor measurements can be observed by the estimator, the system is called a system with observable measurement losses; otherwise, it is called a system with unobservable measurement losses (a UML system). We first obtain the optimal linear estimator (OLE) for multiple-channel UML systems and then establish a necessary and sufficient condition for the stability and convergence of the OLE. We give a tight bound of the estimation performance loss caused by the unobservability of measurement losses. We show that the estimation performance is a monotonically increasing function of the measurement-loss rate and then analytically characterize the relation between the OLE-performance-loss rate and the measurement-loss rate. Finally, numerical examples are provided to show the effectiveness of the proposed OLE, when the measurement-loss status, that is, the private information of measurement losses, cannot be observed.