Mohammadreza Doostmohammadian

On the Genericity Properties in Distributed Estimation: Topology Design and Sensor Placement

In this paper, we consider distributed estimation of linear, discrete-time dynamical systems monitored by a network of agents. We require the agents to exchange information with their neighbors only once per dynamical system time-scale and study the network topology sufficient for distributed observability. To this aim, we provide a novel measurement-based agent classification: Type- α,β, and γ, which leads to the construction of specific graph topologies: <i>G</i>_α and <i>G</i>_β. In particular, in <i>G</i>_α, every Type-α agent has a direct connection to every other agent, whereas, in <i>G</i>_β, every agent has a directed path to every Type-β agent. With the help of these constructs, we formulate an estimator where measurement and predictor-fusion are implemented over <i>G</i>_α and <i>G</i>_β, respectively, and show that the proposed scheme leads to distributed observability, i.e., observability of the distributed estimator. In order to characterize the estimator further, we show that Type-α agents only exist in systems with <i>S</i>-rank (maximal rank of zero/non-zero pattern) deficient system matrices. In other words, systems with full <i>S</i>-rank matrices only have Type-β agents, and thus, a strongly-connected (agent) network is sufficient for full <i>S</i>-rank systems-by the definition of <i>G</i>_β above; however strong-connectivity is not necessary, i.e., there exist weakly-connected networks that result in distributed observability. Furthermore, we show that for <i>S</i> -rank deficient systems, measurement-fusion over <i>G</i>_α is required, and predictor-fusion alone is insufficient. The approach taken in this paper is structural, i.e., we use the concept of structured systems theory and generic observability to derive the results. Finally, we provide an iterative method to compute the local estimator gain at each agent once the observability is ensured using the aforementioned construction.

A sensor placement and network design paradigm for future smart grids

In this paper, we propose a method for sensor placement and communication network design for the purpose of distributed estimation in future smart grids. We use generic observability from structured systems theory to devise sensor placement strategies that are independent of the actual parameter values and are only a function of the underlying structure, i.e., the zero and non-zero pattern, of the physical network. We then use these results to design communication networks among the sensors that ensure observability of the distributed observers formulated on the sensor measurements.

Graph-Theoretic Distributed Inference in Social Networks

We consider distributed inference in social networks where a phenomenon of interest evolves over a given social interaction graph, referred to as the social digraph. We assume that a network of agents monitors certain nodes in the social digraph and the agents rely on inter-agent communication to perform inference. The key contributions include: (i) a novel construction of the distributed estimator and distributed observability from the first principles; (ii) a graph-theoretic agent classification that establishes the importance and role of each agent towards inference; (iii) characterizing the necessary conditions, based on the classification in (ii), on the agent network to achieve distributed observability. Our results are based on structured systems theory and are applicable to any parameter choice of the underlying system matrix as long as the social digraph remains fixed. In other words, any social phenomena that evolves (linearly) over a structure-invariant social digraph may be considered-we refer to such systems as Liner Structure-Invariant (LSI). The aforementioned contributions, (i)-(iii), thus, only require the knowledge of the social digraph (topology) and are independent of the social phenomena. We show the applicability of the results to several real-wold social networks, i.e. social influence among monks, networks of political blogs and books, and a co-authorship graph.

Communication strategies to ensure generic networked observability in multi-agent systems

In this paper, we consider the state estimation in linear dynamical systems when their observations are distributed over a network of agents. We provide a Networked Kalman Filtering (NKF) approach exploring both state and observation fusion. Assuming global observability, we study the structure of the agent communication network in order to stabilize the networked estimation error. In particular, we use structured systems theoretic methods to show that the underlying network may recover observability of locally unobservable agents when the system matrices have full structured rank. In this context, we provide strategies to design communication among the agents and study the effectiveness of these links towards networked observability.

Vulnerability of CPS inference to DoS attacks

We study distributed inference of Cyber Physical Systems (CPS) subject to Denial of Service (DoS). For the purpose of inference, we assume the CPS as a physical-layer (dynamical system) monitored by a cyber-layer (multiagent network). Under DoS, an adversary may disrupt the sensor network monitoring the system either at the underlying communication or at sensors. We investigate countermeasures and CPS resiliency to such failures. We show that the rank-deficiency of the physical system increases the prevalence of hubs in the cyber-layer, and consequently, the vulnerability to the adversary attacks. We provide a power system monitoring example to illustrate our approach.

On the distributed estimation of rank-deficient dynamical systems: A generic approach

In this paper, we consider distributed estimation when the communication time-scale is restricted to the time-scale of the dynamics. It can be shown that this restriction may not guarantee a stable estimation error when the data fusion is implemented only in the observation-space. To address this issue, one has to rely on fusion in the predictor-space, which alone may lead to a stable error only when the system matrix is full S-rank (maximal rank of the zero/non-zero structure). In this paper, we show that when the system matrix is S-rank deficient, predictor-space fusion is insufficient, i.e., the distributed estimator is not observable. In order to recover distributed observability, we provide a novel measurement-based agent classification, and subsequently, define inter-agent communication derived from this classification. The results are based on structured systems theory and the notion of generic observability. Finally, we provide an illustrative example to show the applicability of the proposed schemes using an iterative Linear Matrix Inequality (LMI) approach.

Sensor selection cost optimisation for tracking structurally cyclic systems: a P-order solution

ABSTRACT Measurements and sensing implementations impose certain cost in sensor networks. The sensor selection cost optimisation is the problem of minimising the sensing cost of monitoring a physical (or cyber-physical) system. Consider a given set of sensors tracking states of a dynamical system for estimation purposes. For each sensor assume different costs to measure different (realisable) states. The idea is to assign sensors to measure states such that the global cost is minimised. The number and selection of sensor measurements need to ensure the observability to track the dynamic state of the system with bounded estimation error. The main question we address is how to select the state measurements to minimise the cost while satisfying the observability conditions. Relaxing the observability condition for structurally cyclic systems, the main contribution is to propose a graph theoretic approach to solve the problem in polynomial time. Note that polynomial time algorithms are suitable for large-scale systems as their running time is upper-bounded by a polynomial expression in the size of input for the algorithm. We frame the problem as a linear sum assignment with solution complexity of .

Measurement partitioning and observational equivalence in state estimation

This paper studies observability of linear systems from both algebraic and graph-theoretic arguments, and further draws a parallel between the two. We show that a set of critical measurements (for state-space observability) can be partitioned into two types: α and β. This partitioning is driven by different graphical (or algebraic) methods used to define the corresponding measurements. Subsequently, we describe observational equivalence, i.e., given an α (or β) measurement, say yi, what is the set of measurements equivalent to yi, such that only one measurement in this set is required? Since α and β measurements are cast using different algebraic and graphical characteristics, their equivalence sets are also derived using different algebraic and graph-theoretic principles. The need to make such equivalence arises in areas, e.g., meter placement for power systems, where relevant lines of study include: (a) to guarantee state-space observability with as few sensors as possible; and, (b) to find candidate replacement measurements when a sensor incurs a fault. We illustrate the related concepts on a simple, yet insightful, system digraph.

On the characterization of distributed observability from first principles

In this paper, we derive the distributed observable state from first principles. In particular, we extend the estimation setup to a distributed framework where in addition to the state and sensing, we also have communication among the sensors. We consider that each sensor estimates the entire state-vector to recover its unobservability. Combining the estimates at all of the sensors we arrive at the networked estimator, which subsequently results into the corresponding networked dynamics. We show that the networked dynamics are not just a mere extension of the original dynamics repeated (block-diagonally) to accommodate for each sensor, but belongs to a large class of systems that naturally defines the allowable collaboration among the sensors. Using the redefined distributed estimator (networked dynamics and estimate), we cast the distributed observability and the corresponding estimator.

Topology design in networked estimation: A generic approach

In this paper, we consider networked estimation where asymptotic consensus is replaced with only one fusion iteration between every two successive steps of system dynamics. With this restriction on the fusion, we show that the topology of the communication network plays a key role in the observability (and the error stability) of the estimator. For arbitrary system matrices, algebraic design of the communication topology is challenged with (i) large-scale computation, and (ii) particular fusion rules. To avoid these, structured systems theory and the notion of generic observability are implemented, which are computationally tractable and do not rely on exact fusion rules. We show the stability under weak network connectivity as compared to strong connectivity in the literature. In particular, we do not constrain the system matrix to be generically full rank compared to earlier works and show that for system matrices with rank deficiency (in the generic sense), implementing only state-estimate fusion does not recover the networked observability; thus, output fusion is required.