53 research outputs found
Data-driven and Model-based Verification: a Bayesian Identification Approach
This work develops a measurement-driven and model-based formal verification
approach, applicable to systems with partly unknown dynamics. We provide a
principled method, grounded on reachability analysis and on Bayesian inference,
to compute the confidence that a physical system driven by external inputs and
accessed under noisy measurements, verifies a temporal logic property. A case
study is discussed, where we investigate the bounded- and unbounded-time safety
of a partly unknown linear time invariant system
Observer-based correct-by-design controller synthesis
Current state-of-the-art correct-by-design controllers are designed for
full-state measurable systems. This work first extends the applicability of
correct-by-design controllers to partially observable LTI systems. Leveraging
2nd order bounds we give a design method that has a quantifiable robustness to
probabilistic disturbances on state transitions and on output measurements. In
a case study from smart buildings we evaluate the new output-based
correct-by-design controller on a physical system with limited sensor
information
Prediction error identification of linear dynamic networks with rank-reduced noise
Dynamic networks are interconnected dynamic systems with measured node
signals and dynamic modules reflecting the links between the nodes. We address
the problem of \red{identifying a dynamic network with known topology, on the
basis of measured signals}, for the situation of additive process noise on the
node signals that is spatially correlated and that is allowed to have a
spectral density that is singular. A prediction error approach is followed in
which all node signals in the network are jointly predicted. The resulting
joint-direct identification method, generalizes the classical direct method for
closed-loop identification to handle situations of mutually correlated noise on
inputs and outputs. When applied to general dynamic networks with rank-reduced
noise, it appears that the natural identification criterion becomes a weighted
LS criterion that is subject to a constraint. This constrained criterion is
shown to lead to maximum likelihood estimates of the dynamic network and
therefore to minimum variance properties, reaching the Cramer-Rao lower bound
in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in
Automatica, 4 April 201
Local module identification in dynamic networks with correlated noise: the full input case
The identification of local modules in dynamic networks with known topology
has recently been addressed by formulating conditions for arriving at
consistent estimates of the module dynamics, typically under the assumption of
having disturbances that are uncorrelated over the different nodes. The
conditions typically reflect the selection of a set of node signals that are
taken as predictor inputs in a MISO identification setup. In this paper an
extension is made to arrive at an identification setup for the situation that
process noises on the different node signals can be correlated with each other.
In this situation the local module may need to be embedded in a MIMO
identification setup for arriving at a consistent estimate with maximum
likelihood properties. This requires the proper treatment of confounding
variables. The result is an algorithm that, based on the given network topology
and disturbance correlation structure, selects an appropriate set of node
signals as predictor inputs and outputs in a MISO or MIMO identification setup.
As a first step in the analysis, we restrict attention to the (slightly
conservative) situation where the selected output node signals are predicted
based on all of their in-neighbor node signals in the network.Comment: Extended version of paper submitted to the 58th IEEE Conf. Decision
and Control, Nice, 201
Allocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks
A recent research direction in data-driven modeling is the identification of
dynamic networks, in which measured vertex signals are interconnected by
dynamic edges represented by causal linear transfer functions. The major
question addressed in this paper is where to allocate external excitation
signals such that a network model set becomes generically identifiable when
measuring all vertex signals. To tackle this synthesis problem, a novel graph
structure, referred to as \textit{directed pseudotree}, is introduced, and the
generic identifiability of a network model set can be featured by a set of
disjoint directed pseudotrees that cover all the parameterized edges of an
\textit{extended graph}, which includes the correlation structure of the
process noises. Thereby, an algorithmic procedure is devised, aiming to
decompose the extended graph into a minimal number of disjoint pseudotrees,
whose roots then provide the appropriate locations for excitation signals.
Furthermore, the proposed approach can be adapted using the notion of
\textit{anti-pseudotrees} to solve a dual problem, that is to select a minimal
number of measurement signals for generic identifiability of the overall
network, under the assumption that all the vertices are excited
Single module identifiability in linear dynamic networks
A recent development in data-driven modelling addresses the problem of
identifying dynamic models of interconnected systems, represented as linear
dynamic networks. For these networks the notion network identifiability has
been introduced recently, which reflects the property that different network
models can be distinguished from each other. Network identifiability is
extended to cover the uniqueness of a single module in the network model.
Conditions for single module identifiability are derived and formulated in
terms of path-based topological properties of the network models.Comment: 6 pages, 2 figures, submitted to Control Systems Letters (L-CSS) and
the 57th IEEE Conference on Decision and Control (CDC
Learning linear modules in a dynamic network using regularized kernel-based methods
In order to identify one system (module) in an interconnected dynamic
network, one typically has to solve a Multi-Input-Single-Output (MISO)
identification problem that requires identification of all modules in the MISO
setup. For application of a parametric identification method this would require
estimating a large number of parameters, as well as an appropriate model order
selection step for a possibly large scale MISO problem, thereby increasing the
computational complexity of the identification algorithm to levels that are
beyond feasibility. An alternative identification approach is presented
employing regularized kernel-based methods. Keeping a parametric model for the
module of interest, we model the impulse response of the remaining modules in
the MISO structure as zero mean Gaussian processes (GP) with a covariance
matrix (kernel) given by the first-order stable spline kernel, accounting for
the noise model affecting the output of the target module and also for possible
instability of systems in the MISO setup. Using an Empirical Bayes (EB)
approach the target module parameters are estimated through an
Expectation-Maximization (EM) algorithm with a substantially reduced
computational complexity, while avoiding extensive model structure selection.
Numerical simulations illustrate the potentials of the introduced method in
comparison with the state-of-the-art techniques for local module
identification.Comment: 15 pages, 7 figures, Submitted for publication in Automatica, 12 May
2020. Final version of paper submitted on 06 January 2021 (To appear in
Automatica
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