308 research outputs found
Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm
A supervisory observer is a multiple-model architecture, which estimates the
parameters and the states of nonlinear systems. It consists of a bank of state
observers, where each observer is designed for some nominal parameter values
sampled in a known parameter set. A selection criterion is used to select a
single observer at each time instant, which provides its state estimate and
parameter value. The sampling of the parameter set plays a crucial role in this
approach. Existing works require a sufficiently large number of parameter
samples, but no explicit lower bound on this number is provided. The aim of
this work is to overcome this limitation by sampling the parameter set
automatically using an iterative global optimisation method, called DIviding
RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np
parameter samples where np is the dimension of the parameter set. Then, the
algorithm iteratively adds samples to improve its estimation accuracy.
Convergence guarantees are provided under the same assumptions as in previous
works, which include a persistency of excitation condition. The efficacy of the
supervisory observer with the DIRECT sampling policy is illustrated on a model
of neural populations
Adaptive voltage regulation of an inverter-based power distribution network with a class of droop controllers
The voltage received by each customer connected to a power distribution line
with local controllers (inverters) is regulated to be within a desired margin
through a class of slope-restricted controllers, known conventionally as
\emph{droop} controllers. We adapt the design of the droop controllers
according to the known bounds of the net power consumption of each customer in
each observation time window. A sufficient condition for voltage regulation is
provided for each time window, which guides the design of the droop
controllers, depending on the properties of the distribution line (line
impedances) and the upper bound of all the customers' power consumption during
each time window. The resulting adaptive scheme is verified on a benchmark
model of a European low-voltage network by the CIGRE task force.Comment: This work has been accepted to IFAC World Congress 2020 for
publication under a Creative Commons Licence CC-BY-NC-N
Reachable set-based dynamic quantization for the remote state estimation of linear systems
We employ reachability analysis in designing dynamic quantization schemes for
the remote state estimation of linear systems over a finite date rate
communication channel. The quantization region is dynamically updated at each
transmission instant, with an approximated reachable set of the linear system.
We propose a set-based method using zonotopes and compare it to a norm-based
method in dynamically updating the quantization region. For both methods, we
guarantee that the quantization error is bounded and consequently, the remote
state reconstruction error is also bounded. To the best of our knowledge, the
set-based method using zonotopes has no precedent in the literature and admits
a larger class of linear systems and communication channels, where the
set-based method allows for a longer inter-transmission time and lower bit
rate. Finally, we corroborate our theoretical guarantees with a numerical
example.Comment: This manuscript was accepted for publication at the 62nd IEEE
Conference on Decision and Control (CDC), 202
Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed loop system. The theoretical results are illustrated through numerical simulations
Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed loop system. The theoretical results are illustrated through numerical simulations
A secure state estimation algorithm for nonlinear systems under sensor attacks
The state estimation of continuous-time nonlinear systems in which a subset
of sensor outputs can be maliciously controlled through injecting a potentially
unbounded additive signal is considered in this paper. Analogous to our earlier
work for continuous-time linear systems in \cite{chong2015observability}, we
term the convergence of the estimates to the true states in the presence of
sensor attacks as `observability under attacks', where refers to the
number of sensors which the attacker has access to. Unlike the linear case, we
only provide a sufficient condition such that a nonlinear system is observable
under attacks. The condition requires the existence of asymptotic observers
which are robust with respect to the attack signals in an input-to-state stable
sense. We show that an algorithm to choose a compatible state estimate from the
state estimates generated by the bank of observers achieves asymptotic state
reconstruction. We also provide a constructive method for a class of nonlinear
systems to design state observers which have the desirable robustness property.
The relevance of this study is illustrated on monitoring the safe operation of
a power distribution network.Comment: This paper has been accepted for publication at the 59th IEEE
Conference on Decision and Control, 202
Safety monitoring under stealthy sensor injection attacks using reachable sets
Stealthy sensor injection attacks are serious threats for industrial plants
as they can compromise the plant's integrity without being detected by
traditional fault detectors. In this manuscript, we study the possibility of
revealing the presence of such attacks by monitoring only the control input.
This approach consists in computing an ellipsoidal bound of the input reachable
set. When the control input does not belong to this set, this means that a
stealthy sensor injection attack is driving the plant to critical states. The
problem of finding this ellipsoidal bound is posed as a convex optimization
problem (convex cost with Linear Matrix Inequalities constraints). Our
monitoring approach is tested in simulation
Data-Driven Identification of Attack-free Sensors in Networked Control Systems
This paper proposes a data-driven framework to identify the attack-free
sensors in a networked control system when some of the sensors are corrupted by
an adversary. An operator with access to offline input-output attack-free
trajectories of the plant is considered. Then, a data-driven algorithm is
proposed to identify the attack-free sensors when the plant is controlled
online. We also provide necessary conditions, based on the properties of the
plant, under which the algorithm is feasible. An extension of the algorithm is
presented to identify the sensors completely online against certain classes of
attacks. The efficacy of our algorithm is depicted through numerical examples.Comment: Conference submissio
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
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