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Control design for hybrid systems with TuLiP: The temporal logic planning toolbox
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This tutorial describes TuLiP, the Temporal Logic Planning toolbox, a collection of tools for designing controllers
for hybrid systems from specifications in temporal logic. The
tools support a workflow that starts from a description of
desired behavior, and of the system to be controlled. The
system can have discrete state, or be a hybrid dynamical
system with a mixed discrete and continuous state space. The
desired behavior can be represented with temporal logic and
discrete transition systems. The system description can include
uncontrollable variables that take discrete or continuous values,
and represent disturbances and other environmental factors
that affect the dynamics, as well as communication signals that
affect controller decisions.
A control design problem is solved in phases that involve
abstraction, discrete synthesis, and continuous feedback control.
Abstraction yields a discrete description of system dynamics in
logic. For piecewise affine dynamical systems, this abstraction
is constructed automatically, guided by the geometry of the dynamics
and under logical constraints from the specification. The
resulting logic formulae describe admissible discrete behaviors
that capture both controlled and environment variables. The
discrete description resulting from abstraction is then conjoined
with the desired logic specification. To find a controller, the
toolbox solves a game of infinite duration. Existence of a discrete
(winning) strategy for the controlled variables in this game is a
proof certificate for the existence of a controller for the original
problem, which guarantees satisfaction of the specification. This
discrete strategy, concretized by using continuous controllers,
yields a feedback controller for the original hybrid system. The
toolbox frontend is written in Python, with backends in C,
Python, and Cython.
The tutorial starts with an overview of the theory behind
TuLiP, and of its software architecture, organized into specifi-
cation frontends and backends that implement algorithms for
abstraction, solving games, and interfaces to other tools. Then,
the main elements for writing a specification for input to TuLiP
are introduced. These include logic formulae, discrete transition
systems annotated with predicates, and hybrid dynamical systems,
with linear or piecewise affine continuous dynamics. The
working principles of the algorithms for predicate abstraction
and discrete game solving using nested fixpoints are explained,
by following the input specification through the various transformations
that compile it to a symbolic representation that
scales well to solving large games. The tutorial concludes
with several design examples that demonstrate the toolboxâ€™s
capabilities.
Ioannis Filippidis, Sumanth Dathathri, Scott C. Livingston, Necmiye Ozay, Richard M. Murray
2016e
2016 IEEE Conference on Control Applications (CCA)
fil+16-msc
Conference paper
2016-10-17T15:41:29Z
2457679.1538079
Control design for hybrid systems with TuLiP: The temporal logic planning toolbox
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