Decentralized and Compositional Interconnection Topology Synthesis for Linear Networked Systems

A new necessary and sufficient condition for the controllability of networked linear time-invariant systems is derived, where the network topology is general and the nodes have identical higher dimensional dynamics. The condition is easier to verify, explicitly illustrating how the network topology, node-system dynamics, external control inputs, and inner interactions altogether affect the controllability of the whole networked system. Furthermore, the controllability of the specified Cartesian product networks is revisited, revealing that the necessity of the controllability criterion established in the work presented by Chapman et al. , does not hold. In view of this, a modified, necessary, and sufficient condition is established. The effectiveness of the conditions is demonstrated using several examples.

The ability to maintain state awareness in the face of unexpected and unmodeled errors and threats is a defining feature of a resilient control system. Therefore, in this paper, we study the problem of distributed fault detection and isolation (FDI) in large networked systems with uncertain system models. The linear networked system is composed of interconnected subsystems and may be represented as a graph. The subsystems are represented by nodes, while the edges correspond to the interconnections between subsystems. Considering faults that may occur on the interconnections and subsystems, as our first contribution, we propose a distributed scheme to jointly detect and isolate faults occurring in nodes and edges of the system. As our second contribution, we analyze the behavior of the proposed scheme under model uncertainties caused by the addition or removal of edges. Additionally, we propose a novel distributed FDI scheme based on local models and measurements that is resilient to changes outside of the local subsystem and achieves FDI. Our third contribution addresses the complexity reduction of the distributed FDI method, by characterizing the minimum amount of model information and measurements needed to achieve FDI and by reducing the number of monitoring nodes. The proposed methods can be fused to design a scalable and resilient distributed FDI architecture that achieves local FDI despite unknown changes outside the local subsystem. The proposed approach is illustrated by numerical experiments on the IEEE 118-bus power network benchmark.

In this article, we develop a modular design method of decentralized controllers for linear dynamical network systems, where multiple subcontroller designers aim at individually regulating their local control performance with accessibility only to their respective subsystem models. First, we derive a constrained version of the Youla parameterization that characterizes all retrofit controllers for a single subcontroller, defined as an add-on-type subcontroller that manages a subsystem. The resultant feedback system is kept robustly stable for any variation in the neighboring subsystems, other than the subsystem of interest, provided that the original system is stable prior to implementing the retrofit control. Subsequently, we find out a unique internal structure of the retrofit controllers, assuming that the interaction input signal from the neighboring subsystems is measurable. Furthermore, we show that the simultaneous implementation of multiple retrofit controllers, designed by individual subcontroller designers, can improve the upper bound of the overall control performance. Finally, the practical significance of the method is demonstrated via an illustrative example of frequency regulation using the IEEE 68-bus power system model.

This paper describes applications of graph theory to some of the problems of network analysis and synthesis, starting with the early days of network theory. The first section is devoted to the classical results related to the topological analysis of linear, passive, and transfornerless networks. Then it goes over to contributions dealing with generalization of these methods to networks with mutual couplings and active elements. Appearance of integrated circuits and digital computers provided both motivation and means for studying large-scale systems. A part of the paper is devoted to publications on large-scale network analysis dealing with diacoptics and graph theoretic methods for defining efficient Gaussian elimination algorithms for solution of sparse sets of linear algebraic equations. The part on topological synthesis starts with the early results dealing with relations between the structure and the properties of passive, reciprocal networks without mutual inductances. The last section is devoted to contributions in the field of topological synthesis of pure resistive networks dealing with such topics as conditions of realizability, minimal realizations and bounds on the number of port-terminals.

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

Both the linear recursive networks and the hypercubic networks are known to be self-similar in their interconnection topologies. Here it is shown that multicasting can be efficiently performed on these networks.

This work provides a general framework for the analysis and synthesis of a class of linear networked dynamic systems (NDS). We focus our attention on NDS where the underlying connection topology couples the agents at their outputs. A distinction is made between NDS with homogeneous agent dynamics and NDS with heterogeneous agent dynamics. In the homogeneous setting, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm expression reduces to the Frobenius norm of the underlying connection topology incidence matrix, E(G), scaled by the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of the agents comprising the NDS. In the heterogeneous case, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm becomes the weighted Frobenius norm of the incidence matrix, where the weights appear on the nodes of the graph. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm characterization is then used to synthesize NDS with certain H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance. Specifically, a semi-definite programming solution is presented to design a local controller for each agent when the underlying topology is fixed. A solution using Kruskal's algorithm for finding a minimum weight spanning tree is used to design the optimal NDS topology given fixed agent dynamics.

Chapter 2 - Structural and performance patterns

This paper is concerned with the recursive filtering problem for a class of networked linear time-varying systems subject to the scheduling of the random access protocol (RAP). The communication between the sensor nodes and the remote filter is implemented via a shared network. For the purpose of preventing the data from collisions, only one sensor node is allowed to get access to the network at each time instant. The transmission order of sensor nodes is orchestrated by the RAP scheduling, under which the selected nodes obtaining access to the network could be characterized by a sequence of independent and identically-distributed variables. The aim of the addressed filtering problem is to design a recursive filter such that the filtering error covariance could be minimized by properly designing the filter gain at each time instant. The desired filter gain is calculated recursively by solving two Riccati-like difference equations. Furthermore, the boundedness issue of the corresponding filtering error covariance is investigated. Sufficient conditions are obtained to ensure the lower and upper bounds of the filtering error covariance. Two illustrative examples are given to demonstrate the correctness and effectiveness ofour developed recursive filtering approach.

Multi-agent networked linear dynamic systems have attracted the attention of researchers in power systems, intelligent transportation, and industrial automation. The agents might cooperatively optimize a global performance objective, resulting in social optimization, or try to satisfy their own selfish objectives using a noncooperative differential game. However, in these solutions, large volumes of data must be sent from system states to possibly distant control inputs, thus resulting in high cost of the underlying communication network. To enable economically viable communication, a game-theoretic framework is proposed under the communication cost, or sparsity, constraint, given by the number of communicating state/control input pairs. As this constraint tightens, the system transitions from dense to sparse communication, providing the tradeoff between dynamic system performance and information exchange. Moreover, using the proposed sparsity-constrained distributed social optimization and noncooperative game algorithms, we develop a method to allocate the costs of the communication infrastructure fairly and according to the agents' diverse needs for feedback and cooperation. Numerical results illustrate utilization of the proposed algorithms to enable and ensure economic fairness of wide-area control among power companies.

In this paper, dynamic protocols for multi-agent systems are designed and presented to reach consensus on different scenarios. The architecture of such group of agents are with interconnected scattered topology. In static synchrony communication circumstance, a consensus protocol which is depicted in linear dynamic-system form, is developed to make group of agents finally obtain consensus. The consensus pro- posed can be employed to solve average-consensus problem as well. Faster consensus process is usually required, because in real applications agents should interact (or, make decision) swiftly. Aiming at faster consensus progress and reducing the consensus time, a improved consensus protocol for accelerated consensus is also presented, by adding an acceleration design- parameter. Simulation experiments shows the efficacy and efficiency of such consensus protocols.

LoRaWAN is widely used in information monitoring under star topology. However, for linear topology applications, LoRaWAN protocol requires the introduction of a large number of gateways, which will lead to information asymmetry, energy waste and low network utilization. An energy-saving LoRa linear network system with adaptive transmission parameter is proposed. LoRa multi-hop technology is used for communication between nodes in the system, and Narrow Band Internet of Things module is used to the communicate with cloud platform. The adaptive transmission parameter mechanism is adopted in the system, which improves the adaptability of the linear network to changes in link channel conditions and reduces unnecessary energy consumption. At the same time, the flexibility and robustness of self-organizing networks are enhanced. In addition, optimized duty cycle strategies are employed to further reduce the operating power consumption. After LoRaSim simulation experiments, the results show that in the changing radio channel environment, the adaptive transmission parameter mechanism could achieve a dynamic balance between data extraction rate and energy consumption. After field tests, the results show that the system not only operates stably, but also could reduce the operating energy consumption of the LoRa linear network. The system proposed in this paper is suitable for linear topological structure scenes such as river hydrological monitoring, oil pipeline monitoring and long-distance railway monitoring.

This paper discusses the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control synthesis for discrete-time linear networked systems with time-varying delays in input and output channels. The time-varying delays are assumed to take their values in finite sets, and assumed to be measurable only on line. Our formulation allows the (worst) case of random delays with no stochastic assumption. Considering delays as parameters, we first reformulate the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control problem for networked systems with time-varying delays into that for linear parameter-varying (LPV) systems with jumping parameters. Next, we present a sufficient condition, which is given as a finite set of linear matrix inequalities (LMIs) depending on values of parameters, for synthesizing a gain scheduled output feedback control for LPV systems with jumping parameters, and based on this condition, derive an output feedback controller scheduled with input-output delays. Finally, applying our controller to the networked system composed of the cart and inverted pendulum plant and the input-output channels with random jumping delays, we show that our controller, which does not assume any stochastic property on delays, displays a good performance almost similar to that of the existing stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller.

A ‘linear frequency network’ is a network system which consists of an arbitrary connection of devices, each of which performs a linear transformation on the instantaneous frequency of a signal. Thus a transfer function may be defined relating the output to input instantaneous frequency.Particular networks are investigated. the first is a basic section, producing a ‘self‐adaptive bandpass filter’ which is then applied to a ‘frequency set‐on oscillator’. Such an oscillator is a multimode oscillator where any mode will be stable when excited by a sample of an RF pulse adjacent to the mode. Cascading these basic sections results in an nth‐degree ‘self‐adaptive bandpass filter’ producing a bandpass characteristic which tracks a carrier frequency.Experimental devices in the 400‐600 MHz band are shown to have excellent agreement with theory, and applications to digital RF memories, ESM receivers and frequency memory loops are discussed.

This paper treats an optimization problem of time-varying network topology for continuous-time linear network systems. Although the topology from controllers to nodes has been widely investigated in the literature, this paper alternatively focuses on the topology among nodes. For the cost function, we employ the trace of the controllability Gramian to reduce the required control energy. For the constraint, we introduce an upper bound of the L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm of the data transmission among nodes to find an effective communication schedule. Since the formulated optimization problem is combinatorial, we introduce a convex relaxation for its computational tractability. After reformulating the problem into an optimal control problem where Pontryagin's maximum principle can be applied, we give a sufficient condition under which the relaxation problem gives a solution of the original problem. We finally provide a numerical algorithm based on a derived optimality condition and illustrate the proposed method with an example.