39,448 research outputs found
Towards Scalable Synthesis of Stochastic Control Systems
Formal control synthesis approaches over stochastic systems have received
significant attention in the past few years, in view of their ability to
provide provably correct controllers for complex logical specifications in an
automated fashion. Examples of complex specifications of interest include
properties expressed as formulae in linear temporal logic (LTL) or as automata
on infinite strings. A general methodology to synthesize controllers for such
properties resorts to symbolic abstractions of the given stochastic systems.
Symbolic models are discrete abstractions of the given concrete systems with
the property that a controller designed on the abstraction can be refined (or
implemented) into a controller on the original system. Although the recent
development of techniques for the construction of symbolic models has been
quite encouraging, the general goal of formal synthesis over stochastic control
systems is by no means solved. A fundamental issue with the existing techniques
is the known "curse of dimensionality," which is due to the need to discretize
state and input sets and that results in an exponential complexity over the
number of state and input variables in the concrete system. In this work we
propose a novel abstraction technique for incrementally stable stochastic
control systems, which does not require state-space discretization but only
input set discretization, and that can be potentially more efficient (and thus
scalable) than existing approaches. We elucidate the effectiveness of the
proposed approach by synthesizing a schedule for the coordination of two
traffic lights under some safety and fairness requirements for a road traffic
model. Further we argue that this 5-dimensional linear stochastic control
system cannot be studied with existing approaches based on state-space
discretization due to the very large number of generated discrete states.Comment: 22 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1407.273
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
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