1,141 research outputs found
Low-Complexity Quantized Switching Controllers using Approximate Bisimulation
In this paper, we consider the problem of synthesizing low-complexity
controllers for incrementally stable switched systems. For that purpose, we
establish a new approximation result for the computation of symbolic models
that are approximately bisimilar to a given switched system. The main advantage
over existing results is that it allows us to design naturally quantized
switching controllers for safety or reachability specifications; these can be
pre-computed offline and therefore the online execution time is reduced. Then,
we present a technique to reduce the memory needed to store the control law by
borrowing ideas from algebraic decision diagrams for compact function
representation and by exploiting the non-determinism of the synthesized
controllers. We show the merits of our approach by applying it to a simple
model of temperature regulation in a building
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
In this paper, we propose an approach to controller synthesis for a class of
constrained nonlinear systems. It is based on the use of a hybridization, that
is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined
on a triangulation of the state-space where on each simplex of the
triangulation, the nonlinear dynamics is conservatively approximated by an
affine system subject to disturbances. Except for the disturbances, this
hybridization can be seen as a piecewise affine hybrid system on simplices for
which appealing control synthesis techniques have been developed in the past
decade. We extend these techniques to handle systems subject to disturbances by
synthesizing and coordinating local robust affine controllers defined on the
simplices of the triangulation. We show that the resulting hybrid controller
can be used to control successfully the original constrained nonlinear system.
Our approach, though conservative, can be fully automated and is
computationally tractable. To show its effectiveness in practical applications,
we apply our method to control a pendulum mounted on a cart
Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights
In this paper, we present new results on consensus for continuous-time multi-
agent systems. We introduce the assumptions of persistent connectivity of the
interaction graph and of slow divergence of reciprocal interaction weights.
Persistent connectivity can be considered as the counterpart of the notion of
ultimate connectivity used in discrete- time consensus protocols. Slow
divergence of reciprocal interaction weights generalizes the assumption of
cut-balanced interactions. We show that under these two assumptions, the
continuous-time consensus protocol succeeds: the states of all the agents
converge asymptotically to a common value. Moreover, our proof allows us to
give an estimate of the rate of convergence towards the consensus. We also
provide two examples that make us think that both of our assumptions are tight
Femtosecond spectral electric field reconstruction using coherent transients
We have implemented a new approach for measuring the time-dependent intensity
and phase of ultrashort optical pulses. It is based on the interaction between
shaped pulses and atoms, leading to coherent transients.Comment: 4 pages Accepted in Optics Letter
Symbolic Models for Stochastic Switched Systems: A Discretization and a Discretization-Free Approach
Stochastic switched systems are a relevant class of stochastic hybrid systems
with probabilistic evolution over a continuous domain and control-dependent
discrete dynamics over a finite set of modes. In the past few years several
different techniques have been developed to assist in the stability analysis of
stochastic switched systems. However, more complex and challenging objectives
related to the verification of and the controller synthesis for logic
specifications have not been formally investigated for this class of systems as
of yet. With logic specifications we mean properties expressed as formulae in
linear temporal logic or as automata on infinite strings. This paper addresses
these complex objectives by constructively deriving approximately equivalent
(bisimilar) symbolic models of stochastic switched systems. More precisely,
this paper provides two different symbolic abstraction techniques: one requires
state space discretization, but the other one does not require any space
discretization which can be potentially more efficient than the first one when
dealing with higher dimensional stochastic switched systems. Both techniques
provide finite symbolic models that are approximately bisimilar to stochastic
switched systems under some stability assumptions on the concrete model. This
allows formally synthesizing controllers (switching signals) that are valid for
the concrete system over the finite symbolic model, by means of mature
automata-theoretic techniques in the literature. The effectiveness of the
results are illustrated by synthesizing switching signals enforcing logic
specifications for two case studies including temperature control of a six-room
building.Comment: 25 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1302.386
Approximately bisimilar symbolic models for nonlinear control systems
Control systems are usually modeled by differential equations describing how
physical phenomena can be influenced by certain control parameters or inputs.
Although these models are very powerful when dealing with physical phenomena,
they are less suitable to describe software and hardware interfacing the
physical world. For this reason there is a growing interest in describing
control systems through symbolic models that are abstract descriptions of the
continuous dynamics, where each "symbol" corresponds to an "aggregate" of
states in the continuous model. Since these symbolic models are of the same
nature of the models used in computer science to describe software and
hardware, they provide a unified language to study problems of control in which
software and hardware interact with the physical world. Furthermore the use of
symbolic models enables one to leverage techniques from supervisory control and
algorithms from game theory for controller synthesis purposes. In this paper we
show that every incrementally globally asymptotically stable nonlinear control
system is approximately equivalent (bisimilar) to a symbolic model. The
approximation error is a design parameter in the construction of the symbolic
model and can be rendered as small as desired. Furthermore if the state space
of the control system is bounded the obtained symbolic model is finite. For
digital control systems, and under the stronger assumption of incremental
input-to-state stability, symbolic models can be constructed through a suitable
quantization of the inputs.Comment: Corrected typo
Approximately bisimilar symbolic models for incrementally stable switched systems
Switched systems constitute an important modeling paradigm faithfully
describing many engineering systems in which software interacts with the
physical world. Despite considerable progress on stability and stabilization of
switched systems, the constant evolution of technology demands that we make
similar progress with respect to different, and perhaps more complex,
objectives. This paper describes one particular approach to address these
different objectives based on the construction of approximately equivalent
(bisimilar) symbolic models for switched systems. The main contribution of this
paper consists in showing that under standard assumptions ensuring incremental
stability of a switched system (i.e. existence of a common Lyapunov function,
or multiple Lyapunov functions with dwell time), it is possible to construct a
finite symbolic model that is approximately bisimilar to the original switched
system with a precision that can be chosen a priori. To support the
computational merits of the proposed approach, we use symbolic models to
synthesize controllers for two examples of switched systems, including the
boost DC-DC converter.Comment: 17 page
Compositional abstraction and safety synthesis using overlapping symbolic models
In this paper, we develop a compositional approach to abstraction and safety
synthesis for a general class of discrete time nonlinear systems. Our approach
makes it possible to define a symbolic abstraction by composing a set of
symbolic subsystems that are overlapping in the sense that they can share some
common state variables. We develop compositional safety synthesis techniques
using such overlapping symbolic subsystems. Comparisons, in terms of
conservativeness and of computational complexity, between abstractions and
controllers obtained from different system decompositions are provided.
Numerical experiments show that the proposed approach for symbolic control
synthesis enables a significant complexity reduction with respect to the
centralized approach, while reducing the conservatism with respect to
compositional approaches using non-overlapping subsystems
Triggering mechanism using freely selected sensors for linear time-invariant systems
International audienceExisting event-triggering sampling techniques for state feedback controllers generally use full state information. This may be a source of important computational and communication costs, particularly if sensors are numerous and/or distributed, as the triggering condition needs to be continuously evaluated. We propose an approach to redesign triggering mechanisms for linear time-invariant systems based on limited sensors information, which we freely select, and an internal scalar dynamic variable. We prove that the resulting closed loop system ensures a uniform global exponential stability property and that a uniform minimal inter-execution time is guaranteed. Besides stabilizability, no additional assumption on the system is needed. Guidelines are provided to derive the redesigned triggering conditions using linear matrix inequalities. We show on an academic example that, using a suitable choice of sensors and parameters, inter-execution times using our approach are comparable to those using triggering mechanisms that monitor the full state of the syste
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