132 research outputs found
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
The â„‹_2 Control Problem for Quadratically Invariant Systems With Delays
This technical note gives a new solution to the output feedback â„‹_2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized â„‹_2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finite-dimensional quadratic program. A recursive state-space method for computing the optimal controller based on vectorization is given
H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback
We develop a complete state-space solution to H_2-optimal decentralized
control of poset-causal systems with state-feedback. Our solution is based on
the exploitation of a key separability property of the problem, that enables an
efficient computation of the optimal controller by solving a small number of
uncoupled standard Riccati equations. Our approach gives important insight into
the structure of optimal controllers, such as controller degree bounds that
depend on the structure of the poset. A novel element in our state-space
characterization of the controller is a remarkable pair of transfer functions,
that belong to the incidence algebra of the poset, are inverses of each other,
and are intimately related to prediction of the state along the different paths
on the poset. The results are illustrated by a numerical example.Comment: 39 pages, 2 figures, submitted to IEEE Transactions on Automatic
Contro
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
Stabilizing Queuing Networks with Model Data-Independent Control
Classical queuing network control strategies typically rely on accurate
knowledge of model data, i.e., arrival and service rates. However, such data
are not always available and may be time-variant. To address this challenge, we
consider a class of model data-independent (MDI) control policies that only
rely on traffic state observation and network topology. Specifically, we focus
on the MDI control policies that can stabilize multi-class Markovian queuing
networks under centralized and decentralized policies. Control actions include
routing, sequencing, and holding. By expanding the routes and constructing
piecewise-linear test functions, we derive an easy-to-use criterion to check
the stability of a multi-class network under a given MDI policy. For
stabilizable multi-class networks, we show that a centralized, stabilizing MDI
policy exists. For stabilizable single-class networks, we further show that a
decentralized, stabilizing MDI policy exists. In addition, for both settings,
we construct explicit policies that attain maximal throughput and present
numerical examples to illustrate the results.Comment: Accepted by IEEE Transactions on Control of Network System
An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements
This paper presents a novel design methodology for optimal transmission
policies at a smart sensor to remotely estimate the state of a stable linear
stochastic dynamical system. The sensor makes measurements of the process and
forms estimates of the state using a local Kalman filter. The sensor transmits
quantized information over a packet dropping link to the remote receiver. The
receiver sends packet receipt acknowledgments back to the sensor via an
erroneous feedback communication channel which is itself packet dropping. The
key novelty of this formulation is that the smart sensor decides, at each
discrete time instant, whether to transmit a quantized version of either its
local state estimate or its local innovation. The objective is to design
optimal transmission policies in order to minimize a long term average cost
function as a convex combination of the receiver's expected estimation error
covariance and the energy needed to transmit the packets. The optimal
transmission policy is obtained by the use of dynamic programming techniques.
Using the concept of submodularity, the optimality of a threshold policy in the
case of scalar systems with perfect packet receipt acknowledgments is proved.
Suboptimal solutions and their structural results are also discussed. Numerical
results are presented illustrating the performance of the optimal and
suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network
System
Optimal Decentralized State-Feedback Control with Sparsity and Delays
This work presents the solution to a class of decentralized linear quadratic
state-feedback control problems, in which the plant and controller must satisfy
the same combination of delay and sparsity constraints. Using a novel
decomposition of the noise history, the control problem is split into
independent subproblems that are solved using dynamic programming. The approach
presented herein both unifies and generalizes many existing results
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