Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis

In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear eigenvectors of the differential Hamiltonian matrix. Moreover, under an assumption for the differential Hamiltonian matrix, real symmetricity, regularity, and positive semidefiniteness of solutions are characterized by nonlinear eigenvalues and eigenvectors

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

Reduction of Second-Order Network Systems with Structure Preservation

This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the H2-norms of the transfer function discrepancies. A greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. Then, the reduced-order model is generated by the Petrov-Galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. It is shown that the simplified system preserves an interconnection structure, i.e., it can be again interpreted as a second-order system evolving over a reduced graph. Furthermore, this paper generalizes the definition of network controllability Gramian to second-order network systems. Based on it, we develop an efficient method to compute H2-norms and derive the approximation error between the full-order and reduced-order models. Finally, the approach is illustrated by the example of a small-world network

Krasovskii's Passivity

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit

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/

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