65 research outputs found
Towards a minimal order distributed observer for linear systems
In this paper we consider the distributed estimation problem for
continuous-time linear time-invariant (LTI) systems. A single linear plant is
observed by a network of local observers. Each local observer in the network
has access to only part of the output of the observed system, but can also
receive information on the state estimates of its neigbours. Each local
observer should in this way generate an estimate of the plant state. In this
paper we study the problem of existence of a reduced order distributed
observer. We show that if the observed system is observable and the network
graph is a strongly connected directed graph, then a distributed observer
exists with state space dimension equal to , where
is the number of network nodes, is the state space dimension of the
observed plant, and is the rank of the output matrix of the observed
output received by the th local observer. In the case of a single observer,
this result specializes to the well-known minimal order observer in classical
observer design.Comment: 12 pages, 1 figur
A Filtering Approach for Resiliency of Distributed Observers against Smart Spoofers
A network of observers is considered, where through asynchronous (with
bounded delay) communications, they all estimate the states of a Linear
Time-Invariant (LTI) system. In such setting, a new type of adversarial nodes
might affect the observation process by impersonating the identity of the
regular nodes, which is a violation against communication authenticity. These
adversaries also inherit the capabilities of Byzantine nodes making them more
powerful threats called smart spoofers. We show how asynchronous networks are
vulnerable to smart spoofing attack. In the estimation scheme considered in
this paper, information are flowed from the sets of source nodes, which can
detect a portion of the state variables each, to the other follower nodes. The
regular nodes, to avoid getting misguided by the threats, distributively filter
the extreme values received from the nodes in their neighborhood. Topological
conditions based on graph strong robustness are proposed to guarantee the
convergence. Two simulation scenarios are provided to verify the results
DISTRIBUTED ESTIMATION AND STABILITY OF EVOLUTIONARY GAME DYNAMICS WITH APPLICATIONS TO STUDY OF ANIMAL MOTION
In this dissertation, we consider three problems: in the first we investigate distributed state estimation of linear time-invariant (LTI) plants; in the second we study optimal remote state estimation of Markov processes; while in the third we examine stability of evolutionary game dynamics in large populations.
Problem 1: Consider that an autonomous LTI plant is given and that each member of a network of LTI observers accesses a portion of the output of the plant. The dissemination of information within the network is dictated by a pre-specified directed graph in which each vertex represents an observer. This work proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate using only the portion of the output vector accessible to it and the state estimates of other observers that are available to it, according to the graph. Unlike straightforward high-order solutions in which each observer broadcasts its measurements throughout the network, the average size of the state of each observer in the proposed scheme does not exceed the order of the plant plus one. We determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers. The conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme -- including higher order LTI, nonlinear, and time-varying ones -- subject to the same graph. We apply the proposed scheme to distributed tracking of a group of water buffaloes.
Problem 2: Consider a two-block remote estimation framework in which a sensing unit accesses the full state of a Markov process and decides whether to transmit information about the state to a remotely located estimator given that each transmission incurs a communication cost. The estimator finds the best state estimate of the process using the information received from the sensing unit. The main purpose of this work is to design transmission policies and estimation rules that dictate decision making of the sensing unit and estimator, respectively, and that are optimal for a cost functional which combines the expectation of squared estimation error and communication costs. Our main results establish the existence of transmission policies and estimation rules that are jointly optimal, and propose an iterative procedure to find ones. Our convergence analysis shows that the sequence of sub-optimal solutions generated by the proposed procedure has a convergent subsequence, and the limit of any convergent subsequence is a person-by-person optimal solution. We apply the proposed scheme to remote estimation of location of a water buffalo.
Problem 3: We investigate an energy conservation and dissipation (passivity) aspect of evolutionary dynamics in evolutionary game theory. We define a notion of passivity for evolutionary dynamics, and describe conditions under which dynamics exhibit passivity. For dynamics that are defined on a finite-dimensional state space, we show that the conditions can be characterized in connection with state-space realizations of the dynamics. In addition, we establish stability of passive dynamics in terms of dissipation of stored energy defined by passivity, and present stability results in population games. We provide implications of stability for various passive dynamics both analytically and by means of numerical simulations
A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph
A hybrid observer is described for estimating the state of an channel,
-dimensional, continuous-time, distributed linear system of the form
. The system's state is
simultaneously estimated by agents assuming each agent senses and
receives appropriately defined data from each of its current neighbors.
Neighbor relations are characterized by a time-varying directed graph
whose vertices correspond to agents and whose arcs depict
neighbor relations. Agent updates its estimate of at "event
times" using a local observer and a local parameter
estimator. The local observer is a continuous time linear system whose input is
and whose output is an asymptotically correct estimate of
where a matrix with kernel equaling the unobservable space of .
The local parameter estimator is a recursive algorithm designed to estimate,
prior to each event time , a constant parameter which satisfies the
linear equations , where is a small
positive constant and is the state estimation error of local observer
. Agent accomplishes this by iterating its parameter estimator state
, times within the interval , and by making use of
the state of each of its neighbors' parameter estimators at each iteration. The
updated value of at event time is then . Subject to the assumptions that (i) the neighbor graph
is strongly connected for all time, (ii) the system whose state
is to be estimated is jointly observable, (iii) is sufficiently large, it
is shown that each estimate converges to exponentially fast as
at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro
Design of a distributed finite-time observer using observability decompositions
International audienceIn this paper, a distributed observer is presented to estimate the state of a linear time-invariant plant in finite-time in each observer node. The design is based on a decomposition into locally observable and unobservable substates and on properties of homogeneous systems. Each observer node can reconstruct in finite-time its locally observable substate with its measurements only. Then exploiting the coupling, a finite-time converging observer is constructed for the remaining states by adding the consensus terms. A numerical example illustrates the result
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