Smart abstraction based on iterative cover and non-uniform cells
arxiv(2024)
摘要
We propose a multi-scale approach for computing abstractions of dynamical
systems, that incorporates both local and global optimal control to construct a
goal-specific abstraction. For a local optimal control problem, we not only
design the controller ensuring the transition between every two subsets (cells)
of the state space but also incorporate the volume and shape of these cells
into the optimization process. This integrated approach enables the design of
non-uniform cells, effectively reducing the complexity of the abstraction.
These local optimal controllers are then combined into a digraph, which is
globally optimized to obtain the entire trajectory. The global optimizer
attempts to lazily build the abstraction along the optimal trajectory, which is
less affected by an increase in the number of dimensions. Since the optimal
trajectory is generally unknown in practice, we propose a methodology based on
the RRT* algorithm to determine it incrementally. We illustrate the approach on
a planar nonlinear dynamical system.
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