Temporal Logic Control of Discrete-Time Piecewise Affine Systems

We present a computational framework for automatic synthesis of a feedback control strategy for a discrete-time piecewise affine (PWA) system from a specification given as a linear temporal logic (LTL) formula over an arbitrary set of linear predicates in the system's state variables. Our appro...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2012-06, Vol.57 (6), p.1491-1504
Main Authors: Yordanov, B., Tumova, J., Cerna, I., Barnat, J., Belta, C.
Format: Article
Language:English
Subjects:
Aerospace electronics
Algorithms
Applied sciences
Automata
Computer science
control theory
systems
Control design
Control system synthesis
Control systems
Control theory. Systems
discrete time systems
Educational institutions
Exact sciences and technology
Feedback control
formal specifications
Games
Mathematical analysis
Mathematical models
Perturbation methods
piecewise linear approximation
Strategy
Studies
Temporal logic
Trajectory
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Description
Summary:We present a computational framework for automatic synthesis of a feedback control strategy for a discrete-time piecewise affine (PWA) system from a specification given as a linear temporal logic (LTL) formula over an arbitrary set of linear predicates in the system's state variables. Our approach consists of two main steps. First, by defining appropriate partitions for its state and input spaces, we construct a finite abstraction of the PWA system in the form of a control transition system. Second, by leveraging ideas and techniques from LTL model checking and Rabin games, we develop an algorithm to generate a control strategy for the finite abstraction. While provably correct and robust to state measurements and small perturbations in the applied inputs, the overall procedure is conservative and expensive. The proposed algorithms have been implemented as a software package and made available for download. Illustrative examples are included.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2178328