Project HydLa: Constraint programming for hybrid systems
The third topic is the development of constraint-based technologies
for modeling and verifying hybrid systems, namely systems involving
both continuous and discrete changes. Many physical and biological
systems are naturally modeled as hybrid systems, but the study of
modeling from the perspective of high-level programming languages has
been left unexplored.
Our approach to hybrid systems builds upon the Constraint
Programming paradigm, a paradigm of computing with partial
information developed at the intersection of declarative
programming and artificial intelligence. We seek to establish a
foundational, constraint-based framework for modeling and reasoning
about hybrid systems.
The first embodiment of the above challenge is a modeling language HydLa
and its implementation HyLaGI, both coming with several unique
features. The key feature of HydLa is that its ingredients
consist of popular mathematical and logical notions such as
(in)equations, derivatives, logical implications and temporal operators.
Constraint hierarchy allows you to describe both default and exceptional
behaviors of a system in a concise manner.
HyLaGI is an implementation of HydLa that allows symbolic execution
(simulation) of systems described in HydLa. This has several
consequences: Firstly, HyLaGI is able to handle parameterized hybrid
systems and systems with uncertainties. Secondly, it
nondeterministically explores qualitatively different trajectories
that are free from numerical errors. Thirdly, symbolic parameters
serve as a useful tool for describing and reasoning about systems with
subtle, intricate behaviors.
We are actively exploring the viability of HydLa and HyLaGI towards a
novel tool for cyber-physical systems.