134 research outputs found
Co-design of output feedback laws and event-triggering conditions for linear systems
We present a procedure to simultaneously design the output feedback law and
the event-triggering condition to stabilize linear systems. The closed-loop
system is shown to satisfy a global asymptotic stability property and the
existence of a strictly positive minimum amount of time between two
transmissions is guaranteed. The event-triggered controller is obtained by
solving linear matrix inequalities (LMIs). We then exploit the flexibility of
the method to maximize the guaranteed minimum amount of time between two
transmissions. Finally, we provide a (heuristic) method to reduce the amount of
transmissions, which is supported by numerical simulations
Minimizing the impact of EV charging on the electricity distribution network
The main objective of this paper is to design electric vehicle (EV) charging
policies which minimize the impact of charging on the electricity distribution
network (DN). More precisely, the considered cost function results from a
linear combination of two parts: a cost with memory and a memoryless cost. In
this paper, the first component is identified to be the transformer ageing
while the second one corresponds to distribution Joule losses. First, we
formulate the problem as a non-trivial discrete-time optimal control problem
with finite time horizon. It is non-trivial because of the presence of
saturation constraints and a non-quadratic cost. It turns out that the system
state, which is the transformer hot-spot (HS) temperature here, can be
expressed as a function of the sequence of control variables; the cost function
is then seen to be convex in the control for typical values for the model
parameters. The problem of interest thus becomes a standard optimization
problem. While the corresponding problem can be solved by using available
numerical routines, three distributed charging policies are provided. The
motivation is threefold: to decrease the computational complexity; to model the
important scenario where the charging profile is chosen by the EV itself; to
circumvent the allocation problem which arises with the proposed formulation.
Remarkably, the performance loss induced by decentralization is verified to be
small through simulations. Numerical results show the importance of the choice
of the charging policies. For instance, the gain in terms of transformer
lifetime can be very significant when implementing advanced charging policies
instead of plug-and-charge policies. The impact of the accuracy of the non-EV
demand forecasting is equally assessed.Comment: 6 pages, 3 figures, keywords: electric vehicle charging, electricity
distribution network, optimal control, distributed policies, game theor
Stability analysis of a general class of singularly perturbed linear hybrid systems
Motivated by a real problem in steel production, we introduce and analyze a
general class of singularly perturbed linear hybrid systems with both switches
and impulses, in which the slow or fast nature of the variables can be
mode-dependent. This means that, at switching instants, some of the slow
variables can become fast and vice-versa. Firstly, we show that using a
mode-dependent variable reordering we can rewrite this class of systems in a
form in which the variables preserve their nature over time. Secondly, we
establish, through singular perturbation techniques, an upper bound on the
minimum dwell-time ensuring the overall system's stability. Remarkably, this
bound is the sum of two terms. The first term corresponds to an upper bound on
the minimum dwell-time ensuring the stability of the reduced order linear
hybrid system describing the slow dynamics. The order of magnitude of the
second term is determined by that of the parameter defining the ratio between
the two time-scales of the singularly perturbed system. We show that the
proposed framework can also take into account the change of dimension of the
state vector at switching instants. Numerical illustrations complete our study
A TBLMI Framework for Harmonic Robust Control
The primary objective of this paper is to demonstrate that problems related
to stability and robust control in the harmonic context can be effectively
addressed by formulating them as semidefinite optimization problems, invoking
the concept of infinite-dimensional Toeplitz Block LMIs (TBLMIs). One of the
central challenges tackled in this study pertains to the efficient resolution
of these infinite-dimensional TBLMIs. Exploiting the structured nature of such
problems, we introduce a consistent truncation method that effectively reduces
the problem to a finite-dimensional convex optimization problem. By consistent
we mean that the solution to this finite-dimensional problem allows to closely
approximate the infinite-dimensional solution with arbitrary precision.
Furthermore, we establish a link between the harmonic framework and the time
domain setting, emphasizing the advantages over Periodic Differential LMIs
(PDLMIs). We illustrate that our proposed framework is not only theoretically
sound but also practically applicable to solving H 2 and H harmonic
control design problems. To enable this, we extend the definitions of H 2 and
H norms into the harmonic space, leveraging the concepts of the
harmonic transfer function and the average trace operator for Toeplitz Block
operators. Throughout this paper, we support our theoretical contributions with
a range of illustrative examples that demonstrate the effectiveness of our
approach
Une approche intrinsèque des observateurs linéaires à entrées inconnues
On donne des conditions nécessaires et suffisantes d'existence d'observateurs à entrées inconnues, pour les systèmes linéaires invariants, à temps continu ou discret. Une structure générique valable quel que soit le degré relatif est alors proposé en monovariable, qui peut être étendue au multivariable. Deux exemples, dont l'un avec simulations numériques, sont examinés
A harmonic framework for the identification of linear time-periodic systems
This paper presents a novel approach for the identification of linear
time-periodic (LTP) systems in continuous time. This method is based on
harmonic modeling and consists in converting any LTP system into an equivalent
LTI system with infinite dimension. Leveraging specific harmonic properties, we
demonstrate that solving this infinite-dimensional identification problem can
be reduced to solving a finitedimensional linear least-squares problem. The
result is an approximation of the original solution with an arbitrarily small
error. Our approach offers several significant advantages. The first one is
closely tied to the harmonic system's inherent LTI characteristic, along with
the Toeplitz structure exhibited by its elements. The second advantage is
related to the regularization property achieved through the integral action
when computing the phasors from input and state trajectories. Finally, our
method avoids the computation of signals' derivative. This sets our approach
apart from existing methods that rely on such computations, which can be a
notable drawback, especially in continuous-time settings. We provide numerical
simulations that convincingly demonstrate the effectiveness of the proposed
method, even in scenarios where signals are corrupted by noise
Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach
International audienceThis work focuses on the design of decentralized feedback control gains that aims at optimizing individual costs in a multi-agent synchronization problem. As reported in the literature, the optimal control design for synchronization of agents using local information is NP-hard. Consequently, we relax the problem and use the notion of satisfaction equilibrium from game theory to ensure that each individual cost is guaranteed to be lower than a given threshold. Our main results provide conditions in the form of linear matrix inequalities (LMIs) to check if a given set of control gains are in satisfaction equilibrium i.e. all individual costs are upper-bounded by the imposed threshold. Moreover, we provide an algorithm in order to synthesize gains that are in satisfaction equilibrium. Finally, we illustrate this algorithm with numerical examples
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