1 research outputs found
Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging
and still raise numerous issues so far. In this paper, an original framework
with mixed sets defined as function images of symbol type domains is first
proposed. Syntax and semantics are explicitly distinguished. Then, both
continuous (interval) and discrete (signed, boolean) symbol types are used to
model dependencies through linear and polynomial functions, so leading to mixed
zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes
with typed symbols. Polynotopes can both propagate a mixed encoding of
intervals and describe the behavior of logic gates. A functional completeness
result is given, as well as an inclusion method for elementary nonlinear and
switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a
hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a
stochastic uncertainty paradigm are outlined. Finally, several discrete,
continuous and hybrid numerical examples including comparisons illustrate the
effectiveness of the theoretical results.Comment: 21 pages, 8 figure