111 research outputs found
3 sampled-data control of nonlinear systems
This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research
Time scale modeling for consensus in sparse directed networks with time-varying topologies
The paper considers the consensus problem in large networks represented by
time-varying directed graphs. A practical way of dealing with large-scale
networks is to reduce their dimension by collapsing the states of nodes
belonging to densely and intensively connected clusters into aggregate
variables. It will be shown that under suitable conditions, the states of the
agents in each cluster converge fast toward a local agreement. Local agreements
correspond to aggregate variables which slowly converge to consensus. Existing
results concerning the time-scale separation in large networks focus on fixed
and undirected graphs. The aim of this work is to extend these results to the
more general case of time-varying directed topologies. It is noteworthy that in
the fixed and undirected graph case the average of the states in each cluster
is time-invariant when neglecting the interactions between clusters. Therefore,
they are good candidates for the aggregate variables. This is no longer
possible here. Instead, we find suitable time-varying weights to compute the
aggregate variables as time-invariant weighted averages of the states in each
cluster. This allows to deal with the more challenging time-varying directed
graph case. We end up with a singularly perturbed system which is analyzed by
using the tools of two time-scales averaging which seem appropriate to this
system
A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks
We address the problem of state estimation and attack isolation for general
discrete-time nonlinear systems when sensors are corrupted by (potentially
unbounded) attack signals. For a large class of nonlinear plants and observers,
we provide a general estimation scheme, built around the idea of sensor
redundancy and multi-observer, capable of reconstructing the system state in
spite of sensor attacks and noise. This scheme has been proposed by others for
linear systems/observers and here we propose a unifying framework for a much
larger class of nonlinear systems/observers. Using the proposed estimator, we
provide an isolation algorithm to pinpoint attacks on sensors during sliding
time windows. Simulation results are presented to illustrate the performance of
our tools.Comment: arXiv admin note: text overlap with arXiv:1806.0648
An Unknown Input Multi-Observer Approach for Estimation and Control under Adversarial Attacks
We address the problem of state estimation, attack isolation, and control of
discrete-time linear time-invariant systems under (potentially unbounded)
actuator and sensor false data injection attacks. Using a bank of unknown input
observers, each observer leading to an exponentially stable estimation error
(in the attack-free case), we propose an observer-based estimator that provides
exponential estimates of the system state in spite of actuator and sensor
attacks. Exploiting sensor and actuator redundancy, the estimation scheme is
guaranteed to work if a sufficiently small subset of sensors and actuators are
under attack. Using the proposed estimator, we provide tools for reconstructing
and isolating actuator and sensor attacks; and a control scheme capable of
stabilizing the closed-loop dynamics by switching off isolated actuators.
Simulation results are presented to illustrate the performance of our tools.Comment: arXiv admin note: substantial text overlap with arXiv:1811.1015
A note on input-to-state stabilization for nonlinear sampled-data systems
We provide a framework for the design of stabilizing controllers via approximate discrete-time models for sampled-data nonlinear systems with disturbances. In particular, we present sufficient conditions under which a discrete-time controller that input-to-state stabilizes an approximate discrete-time model of a nonlinear plant with disturbances would also input-to-state stabilize (in an appropriate sense) the exact discrete-time plant model
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
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