107 research outputs found
Consensus as a Nash Equilibrium of a Dynamic Game
Consensus formation in a social network is modeled by a dynamic game of a
prescribed duration played by members of the network. Each member independently
minimizes a cost function that represents his/her motive. An integral cost
function penalizes a member's differences of opinion from the others as well as
from his/her own initial opinion, weighted by influence and stubbornness
parameters. Each member uses its rate of change of opinion as a control input.
This defines a dynamic non-cooperative game that turns out to have a unique
Nash equilibrium. Analytic explicit expressions are derived for the opinion
trajectory of each member for two representative cases obtained by suitable
assumptions on the graph topology of the network. These trajectories are then
examined under different assumptions on the relative sizes of the influence and
stubbornness parameters that appear in the cost functions.Comment: 7 pages, 9 figure, Pre-print from the Proceedings of the 12th
International Conference on Signal Image Technology and Internet-based
Systems (SITIS), 201
Sensor Fault Detection and Isolation in Autonomous Nonlinear Systems Using Neural Network-Based Observers
This paper presents a new observer-based approach to detect and isolate
faulty sensors in industrial systems. Two types of sensor faults are
considered: complete failure and sensor deterioration. The proposed method is
applicable to general autonomous nonlinear systems without making any
assumptions about its triangular and/or normal form, which is usually
considered in the observer design literature. The key aspect of our approach is
a learning-based design of the Luenberger observer, which involves using a
neural network to approximate the injective map that transforms the nonlinear
system into a stable linear system with output injection. This learning-based
Luenberger observer accurately estimates the system's state, allowing for the
detection of sensor faults through residual generation. The residual is
computed as the norm of the difference between the system's measured output and
the observer's predicted output vectors. Fault isolation is achieved by
comparing each sensor's measurement with its corresponding predicted value. We
demonstrate the effectiveness of our approach in capturing and isolating sensor
faults while remaining robust in the presence of measurement noise and system
uncertainty. We validate our method through numerical simulations of sensor
faults in a network of Kuramoto oscillators
Feedback Design for Devising Optimal Epidemic Control Policies
For reliable epidemic monitoring and control, this paper proposes a feedback
mechanism design to effectively cope with data and model uncertainties. Using
past epidemiological data, we describe methods to estimate the parameters of
general epidemic models. Because the data could be noisy, the estimated
parameters may not be accurate. Therefore, under uncertain parameters and noisy
measurements, we provide an observer design method for robust state estimation.
Then, using the estimated model and state, we devise optimal control policies
by minimizing a predicted cost functional. Finally, the effectiveness of the
proposed method is demonstrated through its implementation on a modified SIR
epidemic model
Secure Set-Based State Estimation for Linear Systems under Adversarial Attacks on Sensors
When a strategic adversary can attack multiple sensors of a system and freely
choose a different set of sensors at different times, how can we ensure that
the state estimate remains uncorrupted by the attacker? The existing literature
addressing this problem mandates that the adversary can only corrupt less than
half of the total number of sensors. This limitation is fundamental to all
point-based secure state estimators because of their dependence on algorithms
that rely on majority voting among sensors. However, in reality, an adversary
with ample resources may not be limited to attacking less than half of the
total number of sensors. This paper avoids the above-mentioned fundamental
limitation by proposing a set-based approach that allows attacks on all but one
sensor at any given time. We guarantee that the true state is always contained
in the estimated set, which is represented by a collection of constrained
zonotopes, provided that the system is bounded-input-bounded-state stable and
redundantly observable via every combination of sensor subsets with size equal
to the number of uncompromised sensors. Additionally, we show that the
estimated set is secure and stable irrespective of the attack signals if the
process and measurement noises are bounded. To detect the set of attacked
sensors at each time, we propose a simple attack detection technique. However,
we acknowledge that intelligently designed stealthy attacks may not be detected
and, in the worst-case scenario, could even result in exponential growth in the
algorithm's complexity. We alleviate this shortcoming by presenting a range of
strategies that offer different levels of trade-offs between estimation
performance and complexity
Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems
The design of Luenberger observers for nonlinear systems involves state
transformation to another coordinate system where the dynamics are
asymptotically stable and linear up to output injection. The observer then
provides a state estimate in the original coordinates by inverting the
transformation map. For general nonlinear systems, however, the main challenge
is to find such a transformation and to ensure that it is injective. This paper
addresses this challenge by proposing a learning method that employs supervised
physics-informed neural networks to approximate both the transformation and its
inverse. It is shown that the proposed method exhibits better generalization
capabilities than other contemporary methods. Moreover, the observer is shown
to be robust under the neural network's approximation error and the system
uncertainties
Secure State Estimation against Sparse Attacks on a Time-varying Set of Sensors
This paper studies the problem of secure state estimation of a linear
time-invariant (LTI) system with bounded noise in the presence of sparse
attacks on an unknown, time-varying set of sensors. In other words, at each
time, the attacker has the freedom to choose an arbitrary set of no more that
sensors and manipulate their measurements without restraint. To this end,
we propose a secure state estimation scheme and guarantee a bounded estimation
error subject to -sparse observability and a mild, technical assumption
that the system matrix has no degenerate eigenvalues. The proposed scheme
comprises a design of decentralized observer for each sensor based on the local
observable subspace decomposition. At each time step, the local estimates of
sensors are fused by solving an optimization problem to obtain a secure
estimation, which is then followed by a local detection-and-resetting process
of the decentralized observers. The estimation error is shown to be
upper-bounded by a constant which is determined only by the system parameters
and noise magnitudes. Moreover, we optimize the detector threshold to ensure
that the benign sensors do not trigger the detector. The efficacy of the
proposed algorithm is demonstrated by its application on a benchmark example of
IEEE 14-bus system
Average observability of large-scale network systems
International audienceThis paper addresses observability and detectability of the average state of a network system when few gateway nodes are available. To reduce the complexity of the problem, the system is transformed to a lower dimensional state space by aggregation. The notions of average observability and average detectability are then defined, and the respective necessary and sufficient conditions are provided
Scale-free estimation of the average state in large-scale systems
International audienceThis paper provides a computationally tractable necessary and sufficient condition for the existence of an average state observer for large-scale linear time-invariant (LTI) systems. Two design procedures, each with its own significance, are proposed. When the necessary and sufficient condition is not satisfied, a methodology is devised to obtain an optimal asymptotic estimate of the average state. In particular, the estimation problem is addressed by aggregating the unmeasured states of the original system and obtaining a projected system of reduced dimension. This approach reduces the complexity of the estimation task and yields an observer of dimension one. Moreover, it turns out that the dimension of the system also does not affect the upper bound on the estimation error
Modeling and Control of COVID-19 Epidemic through Testing Policies
Testing for the infected cases is one of the most important mechanisms to
control an epidemic. It enables to isolate the detected infected individuals,
thereby limiting the disease transmission to the susceptible population.
However, despite the significance of testing policies, the recent literature on
the subject lacks a control-theoretic perspective. In this work, an epidemic
model that incorporates the testing rate as a control input is presented. The
proposed model differentiates the undetected infected from the detected
infected cases, who are assumed to be removed from the disease spreading
process in the population. First, the model is estimated and validated for
COVID-19 data in France. Then, two testing policies are proposed, the so-called
best-effort strategy for testing (BEST) and constant optimal strategy for
testing (COST). The BEST policy is a suppression strategy that provides a lower
bound on the testing rate such that the epidemic switches from a spreading to a
non-spreading state. The COST policy is a mitigation strategy that provides an
optimal value of testing rate that minimizes the peak value of the infected
population when the total stockpile of tests is limited. Both testing policies
are evaluated by predicting the number of active intensive care unit (ICU)
cases and the cumulative number of deaths due to COVID-19.Comment: 49 pages, 22 figure
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