4,161 research outputs found
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
Stabilizing switching signals: a transition from point-wise to asymptotic conditions
Characterization of classes of switching signals that ensure stability of
switched systems occupies a significant portion of the switched systems
literature. This article collects a multitude of stabilizing switching signals
under an umbrella framework. We achieve this in two steps: Firstly, given a
family of systems, possibly containing unstable dynamics, we propose a new and
general class of stabilizing switching signals. Secondly, we demonstrate that
prior results based on both point-wise and asymptotic characterizations follow
our result. This is the first attempt in the switched systems literature where
these switching signals are unified under one banner.Comment: 7 page
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
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
A characterization of switched linear control systems with finite L 2 -gain
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of
Barabanov norm and extremal trajectory to classes of switching signals that are
not closed under concatenation. We use these tools to prove that the finiteness
of the L2-gain is equivalent, for a large set of switched linear control
systems, to the condition that the generalized spectral radius associated with
any minimal realization of the original switched system is smaller than one
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