29 research outputs found
Minimum Number of Probes for Brain Dynamics Observability
In this paper, we address the problem of placing sensor probes in the brain
such that the system dynamics' are generically observable. The system dynamics
whose states can encode for instance the fire-rating of the neurons or their
ensemble following a neural-topological (structural) approach, and the sensors
are assumed to be dedicated, i.e., can only measure a state at each time. Even
though the mathematical description of brain dynamics is (yet) to be
discovered, we build on its observed fractal characteristics and assume that
the model of the brain activity satisfies fractional-order dynamics.
Although the sensor placement explored in this paper is particularly
considering the observability of brain dynamics, the proposed methodology
applies to any fractional-order linear system. Thus, the main contribution of
this paper is to show how to place the minimum number of dedicated sensors,
i.e., sensors measuring only a state variable, to ensure generic observability
in discrete-time fractional-order systems for a specified finite interval of
time. Finally, an illustrative example of the main results is provided using
electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720
A Structured Systems Approach for Optimal Actuator-Sensor Placement in Linear Time-Invariant Systems
In this paper we address the actuator/sensor allocation problem for linear
time invariant (LTI) systems. Given the structure of an autonomous linear
dynamical system, the goal is to design the structure of the input matrix
(commonly denoted by ) such that the system is structurally controllable
with the restriction that each input be dedicated, i.e., it can only control
directly a single state variable. We provide a methodology that addresses this
design question: specifically, we determine the minimum number of dedicated
inputs required to ensure such structural controllability, and characterize,
and characterizes all (when not unique) possible configurations of the
\emph{minimal} input matrix . Furthermore, we show that the proposed
solution methodology incurs \emph{polynomial complexity} in the number of state
variables. By duality, the solution methodology may be readily extended to the
structural design of the corresponding minimal output matrix (commonly denoted
by ) that ensures structural observability.Comment: 8 pages, submitted for publicatio
On the Complexity of the Constrained Input Selection Problem for Structural Linear Systems
This paper studies the problem of, given the structure of a linear-time
invariant system and a set of possible inputs, finding the smallest subset of
input vectors that ensures system's structural controllability. We refer to
this problem as the minimum constrained input selection (minCIS) problem, since
the selection has to be performed on an initial given set of possible inputs.
We prove that the minCIS problem is NP-hard, which addresses a recent open
question of whether there exist polynomial algorithms (in the size of the
system plant matrices) that solve the minCIS problem. To this end, we show that
the associated decision problem, to be referred to as the CIS, of determining
whether a subset (of a given collection of inputs) with a prescribed
cardinality exists that ensures structural controllability, is NP-complete.
Further, we explore in detail practically important subclasses of the minCIS
obtained by introducing more specific assumptions either on the system dynamics
or the input set instances for which systematic solution methods are provided
by constructing explicit reductions to well known computational problems. The
analytical findings are illustrated through examples in multi-agent
leader-follower type control problems
On the Limited Communication Analysis and Design for Decentralized Estimation
This paper pertains to the analysis and design of decentralized estimation
schemes that make use of limited communication. Briefly, these schemes equip
the sensors with scalar states that iteratively merge the measurements and the
state of other sensors to be used for state estimation. Contrarily to commonly
used distributed estimation schemes, the only information being exchanged are
scalars, there is only one common time-scale for communication and estimation,
and the retrieval of the state of the system and sensors is achieved in
finite-time. We extend previous work to a more general setup and provide
necessary and sufficient conditions required for the communication between the
sensors that enable the use of limited communication decentralized
estimation~schemes. Additionally, we discuss the cases where the sensors are
memoryless, and where the sensors might not have the capacity to discern the
contributions of other sensors. Based on these conditions and the fact that
communication channels incur a cost, we cast the problem of finding the minimum
cost communication graph that enables limited communication decentralized
estimation schemes as an integer programming problem.Comment: Updates on the paper in CDC 201