In this paper, we consider composite networks formed from the Kronecker product of smaller networks. We find the observability and controllability properties of the product network from those of its constituent smaller networks. The overall network is modeled as a Linear-Structure-Invariant (LSI) dynamical system where the underlying matrices have a fixed zero/non-zero structure but the non-zero elements are potentially time-varying. This approach allows to model the system parameters as free variables whose values may only be known within a certain tolerance. We particularly look for minimal sufficient conditions on the observability and controllability of the composite network, which have a direct application in distributed estimation and in the design of networked control systems. The methodology in this paper is based on the structured systems analysis and graph theory, and therefore, the results are generic, i.e., they apply to almost all non-zero choices of free parameters. We show the controllability/observability results for composite product networks resulting from full structural-rank systems and self-damped networks. We provide an illustrative example of estimation based on Kalman filtering over a composite network to verify our results.
This paper considers distributed estimation of linear systems when the state observations are corrupted with Gaussian noise of unbounded support and under possible random adversarial attacks. We consider sensors equipped with single time-scale estimators and local chi-square ($χ^2$) detectors to simultaneously opserve the states, share information, fuse the noise/attack-corrupted data locally, and detect possible anomalies in their own observations. While this scheme is applicable to a wide variety of systems associated with full-rank (invertible) matrices, we discuss it within the context of …
Control-Theoretic View of Neural ODEs: Empirical Controllability and Observability
The University of Alabama in Huntsville（阿拉巴马大学亨茨维尔分校）；AI, Autonomy, Resilience, Control (AARC) Lab at the Department of Electrical and Computer Engineering, The University of Alabama in Huntsville（阿拉巴马大学亨茨维尔分校电气与计算机工程系自主、韧性控制实验室）
This paper provides the extension of the observability rank condition and the extension of the controllability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability and controllability, only account for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this paper, the general analytic conditions are provided. The paper shows that both these two new conditions (the extended observability rank condition and the extended controllability rank condition) reduce to the well…
In this paper, we study large-scale networks in terms of observability and controllability. In particular, we compare the number of unmatched nodes in two main types of Scale-Free (SF) networks: the Barab{á}si-Albert (BA) model and the Holme-Kim (HK) model. Comparing the two models based on theory and simulation, we discuss the possible relation between clustering coefficient and the number of unmatched nodes. In this direction, we propose a new algorithm to reduce the number of unmatched nodes via link addition. The results are significant as one can reduce the number of unmatched nodes and t…
In this paper, the controllability and observability of linear multi-agent systems over matrix-weighted signed networks are analyzed. Firstly, the definition of equitable partition of matrix-weighted signed multi-agent system is given, and the upper bound of controllable subspace and a necessary condition of controllability are obtained by combining the restriction conditions of the coefficient matrix and matrix weight for the case of fixed and switching topologies, respectively.The influence of different selection methods of coefficient matrices on the results is discussed. Secondly, for the …
Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability, observability, and controller and observer design. This note describes a graphical mechanism to transform a system expressed in observability form into its observer form based on elementary block diagram manipulations, a technique whose pedagogical usefulness tends to be overlooked. Given the well-known duality principle in linear systems with respect to controllabi…
Nonlinear Model Reduction in Power Systems by Balancing of Empirical Controllability and Observability Covariances
Energy Systems Division, Argonne National Laboratory（阿贡国家实验室能源系统部）；Department of Electrical Engineering, Guangxi University（广西大学电气工程学院）；Energy and Transportation Sciences Division, Oak Ridge National Laboratory（橡树岭国家实验室能源与交通科学部）
Structural accessibility and structural observability of nonlinear networked systems
CONACyT - Institute of Mathematics, Universidad Nacional Autonoma de Mexico（墨西哥国立自治大学数学研究所）；Institute of Mathematics, Universidad Nacional Autonoma de Mexico（墨西哥国立自治大学数学研究所）；Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004（南特数字科学实验室）
The School of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Birkbeck, University of London（伦敦大学伯贝克学院）；University of Luxembourg（卢森堡大学）
In this paper, given a linear time-invariant strongly connected network, we study the problem of determining the minimum number of state variables that need to be simultaneously actuated and measured to ensure structural controllability and observability, respectively. This problem is fundamental in the design of multi-agent systems, where there are economic constraints in the decision of which agents to equip with a more costly on-board system that will allow the agent to have both actuation and sensing capabilities. Despite the combinatorial nature of this problem, we present a solution that…
