Towards time-varying proximal dynamics in Multi-Agent Network Games

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled as inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we provide an operator-theoretic characterization of convergence with a time-invariant communication network. For the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure

Design of Privacy-Preserving Dynamic Controllers:Special Issue of "Security and Privacy of Distributed Algorithms and Network Systems"

As a quantitative criterion for privacy of “mechanisms” in the form of data-generating processes, the concept of differential privacy was first proposed in computer science and has later been applied to linear dynamical systems. However, differential privacy has not been studied in depth together with other properties of dynamical systems, and it has not been fully utilized for controller design. In this paper, first we clarify that a classical concept in systems and control, input observability (sometimes referred to as left invertibility) has a strong connection with differential privacy. In particular, we show that the Gaussian mechanism can be made highly differentially private by adding small noise if the corresponding system is less input observable. Next, enabled by our new insight into privacy, we develop a method to design dynamic controllers for the classic tracking control problem while addressing privacy concerns. We call the obtained controller through our design method the privacy-preserving controller. The usage of such controllers is further illustrated by an example of tracking the prescribed power supply in a DC microgrid installed with smart meters while keeping the electricity consumers' tracking errors private

Revisit Input Observability:A New Approach to Attack Detection and Privacy Preservation

Models for attack detection and privacy preservation of linear systems can be formulated in terms of their input observability, which is also called the left invertibility of their transfer function matrices. While left invertibility is a classical concept, we re-examine it from the perspectives of security and privacy. In this paper, for discrete-time linear systems, we design an input observer in order to detect attacks. We also present the input observability Gramian, which is used to characterize the systems' privacy level; it is shown that a strong connection can be made between the input observability Gramian and a standard privacy concept called differential privacy

Effects of Quantization and Dithering in Privacy Analysis for a Networked Control System

In digital communication networks, typically information is sent after quantization. When such quantized information is used by controllers, it is known that quantization is very likely to degenerate control performance. In contrast, we show in this paper the interesting finding that quantization may improve privacy performance of the networked subsystems under control. Namely, there is a trade-off between control and privacy performances determined by the quantization step. In this paper, we look at a dither (also called random dithered quantizer) as a possible tool to improve both control and privacy performances for networked systems. We review some known improved control performances such as in sampling, and then further discuss the effects of a dither in privacy analysis

Structural Accessibility and Its Applications to Complex Networks Governed by Nonlinear Balance Equations

We define and then study the structural controllability and observability for a class of complex networks whose dynamics are governed by the nonlinear balance equations. Although related notions of observability for such complex networks have been studied before and in particular, necessary conditions have been reported to select sensor nodes in order to render such a given network observable, there still remain various challenging open problems, especially from the systems and control point of view. The reason is partly that driver and sensor node selection problems for nonlinear complex networks have not been studied systematically, which differs greatly from the relatively comprehensive mathematical development for the linear counterpart. In this paper, based on our refined notions of structural controllability and observability, we construct their necessary conditions for nonlinear complex networks, which are further applied to those networks governed by nonlinear balance equations in order to develop a systematic driver node selection method. Furthermore, we establish a connection between our necessary conditions for structural observability and the conventional sensor node selection method

Effects of Quantization and Dithering in Privacy Analysis for a Networked Control System

In digital communication networks, typically information is sent after quantization. When such quantized information is used by controllers, it is known that quantization is very likely to degenerate control performance. In contrast, we show in this paper the interesting finding that quantization may improve privacy performance of the networked subsystems under control. Namely, there is a trade-off between control and privacy performances determined by the quantization step. In this paper, we look at a dither (also called random dithered quantizer) as a possible tool to improve both control and privacy performances for networked systems. We review some known improved control performances such as in sampling, and then further discuss the effects of a dither in privacy analysis.<br/

Modular control under privacy protection:Fundamental trade-offs

In privacy-preserving controller design, there is usually a trade-off between the privacy level and control performances, and we show in this paper that this trade-off in particular determines a lower bound on the differential privacy level of the closed-loop system. The control task we consider is reference tracking in a plug-and-play setting, and the plant under control is a networked system of modules, each of which has no access to the models of the others. For a module, we first identify the whole set of tracking local controllers based on the Youla parametrization. At the same time, each module, to protect its own privacy, tries to prevent the other interconnected modules to identify its private information; in this context, for example, the tracking reference signal (say, the target production amount if each module is a workshop in a factory) can be viewed as a piece of private information. Each module can tune the parameters of its local controller to increase the privacy level of its reference signal. However, if the distribution of Laplace (resp. uniform) noise is fixed, the differential privacy level of a Laplace (resp. uniform) mechanism cannot be further improved from a ceiling value no matter how one tunes parameters. In other words, for modular systems under local reference tracking control, there is a lower bound on the differential privacy level.</p

A Fundamental Performance Limit of Cloud-based Control in Terms of Differential Privacy Level

In this paper, we address a privacy issue raised by cloud based control. In a cloud based control framework, a plant typically has no access to the models of the cloud system and other plants connected via the cloud system. Under restricted information, the plant is required to design its local controller for achieving control objectives. As a control objective, we consider a tracking problem, and for constant reference signals, a class of tracking controllers is identified based on Youla parametrization. More importantly, as local tracking controllers are implemented, there is a possibility that the cloud system or other plants connected via the cloud system may be able to identify private information of the plant by using the collected signal from the plant; for example, the reference signal (say, the target production amount) of the plant can be viewed as a piece of private information. In order to evaluate the privacy level of the reference signal, we employ the concept of differential privacy. For the Laplace mechanism induced by the entire system, we show that the differential privacy level cannot be further improved from a ceiling value for any parameters of the local controller. In other words, there is a performance limit in terms of differential privacy level, which is determined by the plant and cloud system only.</p