This paper formulates a framework for the analysis and distributed control of interconnected systems from the behavioural perspective. The discussions are carried out from the viewpoint of set theory and the results are completely representation-free. The core of a dynamical system can be represented as the set of all trajectories admissible through the system and interconnections are interpreted as constraints on the choice of trajectories. We develop a structure in which the interconnected behaviour can be directly built from the behaviours of the subsystems in an explicit way without any presumed forms of representations. We show that the interconnected behaviour can also be fully obtained from local observations of the subsystem. Furthermore, we develop the necessary and sufficient conditions for the existence of distributed controller behaviours and their explicit construction. Due to the entirely representation-free nature of this framework, it unites various representations and descriptions of features of dynamical systems (e.g. models, dissipativity, data, etc.) as behaviours, allowing for the formation of a unified platform for the analysis and distributed control for interconnected systems.
The problem of mitigating maliciously injected signals in interconnected systems is dealt with in this paper. We consider the class of covert attacks, as they are stealthy and cannot be detected by conventional means in centralized settings. Distributed architectures can be leveraged for revealing such stealthy attacks by exploiting communication and local model knowledge. We show how such detection schemes can be improved to estimate the action of an attacker and we propose an accommodation scheme in order to mitigate or neutralize abnormal behavior of a system under attack.
This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2-gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows relaxing the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t most existing approaches. We show how to decom…
This paper is concerned with the problem of distributed estimation for time-varying interconnected dynamic systems with arbitrary coupling structures. To guarantee the robustness of the designed estimators, novel distributed stability conditions are proposed with only local information and the information from neighbors. Then, simplified stability conditions which do not require timely exchange of neighbors' estimator gain information is further developed for systems with delayed communication. By merging these subsystem-level stability conditions and the optimization-based estimator gain desi…
The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complex…
This paper proposed a distributed filter for spatially interconnected systems (SISs), which considers missing measurements in the sensors of sub-systems. An SIS is established by many similar sub-systems that directly interact or communicate with connective neighbors. Despite that the interactions are simple and tractable, the overall SIS can perform rich and complex behaviors. In actual projects, sensors of sub-systems in a sensor network may break down sometimes, which causes parts of the measurements unavailable unexpectedly. In this work, distributed characteristics of SISs are described b…
The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that …
This paper presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the…
Resilient Distributed Energy Management for Systems of Interconnected Microgrids
Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Institut de Robòtica i Informàtica Industrial (CSIC-UPC)（机器人与工业信息学研究所）；Tokyo Institute of Technology（东京工业大学）；University of Seville（塞维利亚大学）
A graph theoretic framework recently has been proposed to stabilize interconnected multiagent systems in a distributed fashion, while systematically capturing the architectural aspect of cyber-physical systems with separate agent or physical layer and control or cyber layer. Based on that development, in addition to the modeling uncertainties over the agent layer, we consider a scenario where the control layer is subject to the denial of service attacks. We propose a step-by-step procedure to design a control layer that, in the presence of the aforementioned abnormalities, guarantees a level o…
A design framework recently has been developed to stabilize interconnected multiagent systems in a distributed manner, and systematically capture the architectural aspect of cyber-physical systems. Such a control theoretic framework, however, results in a stabilization protocol which is passive with respect to the cyber attacks and conservative regarding the guaranteed level of resiliency. We treat the control layer topology and stabilization gains as the degrees of freedom, and develop a mixed control and cybersecurity design framework to address the above concerns. From a control perspective…
Distributed Verification of Structural Controllability for Linear Time-Invariant Systems
Instituto Superior Técnico, University of Lisbon（里斯本大学高等理工学院）；Carnegie Mellon University（卡内基梅隆大学）；University of Porto (FEUP)（波尔图大学）；KTH Royal Institute of Technology（皇家理工学院）
We develop a novel decentralized control method for a network of perturbed linear systems with dynamical couplings subject to Signal Temporal Logic (STL) specifications. We first transform the STL requirements into set containment problems and then we develop controllers to solve these problems. Our approach is based on treating the couplings between subsystems as disturbances, which are bounded sets that the subsystems negotiate in the form of parametric assume-guarantee contracts. The set containment requirements and parameterized contracts are added to the subsystems' constraints. We introd…
In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the con…
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
United Technologies Research Center（联合技术研究中心）；AIMdyn Inc.（AIMdyn公司）；California Institute of Technology（加州理工学院）；University of California, Santa Barbara（加利福尼亚大学圣塔芭芭拉分校）
We present a distributed control law to assemble a cluster of satellites into an equally-spaced, planar constellation in a desired circular orbit about a planet. We assume each satellite only uses local information, transmitted through communication links with neighboring satellites. The same control law is used to maintain relative angular positions in the presence of disturbance forces. The stability of the constellation in the desired orbit is proved using a compositional approach. We first show the existence and uniqueness of an equilibrium of the interconnected system. We then certify eac…
In this paper, an alternating direction method of multipliers based novel distributed wide-area control architecture is proposed for damping the interarea oscillations. In this approach, first, an interconnected power system is divided into areas based on coherency grouping. Second, local processors are assigned on each area that estimate a black-box transfer function model based on Lagrange multipliers using measurements. These local area processors are then used to estimate a global transfer function model of the power system based on a consensus algorithm through a global processor. After c…
Distributed component-level modeling and control of energy dynamics in electric power systems
Massachusetts Institute of Technology（麻省理工学院）；SmartGridz；Laboratory for Information and Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
Universidad de Zaragoza（萨拉戈萨大学）；University of California San Diego（加州大学圣地亚哥分校）
This paper presents LEMURS, an algorithm for learning scalable multi-robot control policies from cooperative task demonstrations. We propose a port-Hamiltonian description of the multi-robot system to exploit universal physical constraints in interconnected systems and achieve closed-loop stability. We represent a multi-robot control policy using an architecture that combines self-attention mechanisms and neural ordinary differential equations. The former handles time-varying communication in the robot team, while the latter respects the continuous-time robot dynamics. Our representation is di…
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system, this renders the optimal controller a centralized one. The interconnected nature of a network system often demands a distributed controller, where different components of the system are controlled based only on local information. Unlike the classical centralized case, obtaining the optimal distributed controller is usually an intractable problem. Thus, we ado…
We address the multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected over a network topology. A measure of mean overall node state uncertainty evaluated over a finite period is to be minimized by controlling the motion of a cooperating team of agents. To address this problem, we propose an event-driven receding horizon control approach that is computationally efficient, distributed and on-line. The proposed controller differs from the existing on-line gradient-based parametric controllers and off-line greedy cycle search methods that often lead to either …
The work done in this paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the traditional method of organizing large scattered networks into smaller interconnected clusters to optimize information flow within the network. The complex Laplacian-based approach results in a hierarchical structure, with formation of a meta-cluster leading other clusters in the network. The proposed formulation enables flexibility to constrain the eigen spectra…
Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems
Mathematics and Computer Science Division, Argonne National Laboratory（阿贡国家实验室数学与计算机科学部）；California Institute of Technology（加州理工学院）；Department of Electrical and Computer Engineering, Carnegie Mellon University（卡内基梅隆大学电气与计算机工程系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
