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Smart abstraction based on iterative cover and non-uniform cells
Dynamical Systems · Submitted 4 Mar 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we provide a tractable implementation of this algorithm for the optimal control of L-smooth nonlinear dynamical systems.
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The abstract, sentence by sentence
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. Finally, we provide a tractable implementation of this algorithm for the optimal control of L-smooth nonlinear dynamical systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.99 | 0.88 | 0.27 | asserted 0.99 |
| s1 | 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. | method 0.85 | 0.92 | 0.07 | asserted 1.00 |
| s2 | This integrated approach enables the design of non-uniform cells, effectively reducing the complexity of the abstraction. | interpretation 0.50 | 0.81 | 0.21 | asserted 0.98 |
| s3 | These local optimal controllers are then combined into a digraph, which is globally optimized to obtain the entire trajectory. | method 0.99 | 0.83 | 0.09 | asserted 1.00 |
| s4 | 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. | interpretation 0.36 | 0.59 | 0.13 | asserted 0.88 |
| s5 | Since the optimal trajectory is generally unknown in practice, we propose a methodology based on the RRT* algorithm to determine it incrementally. | method 0.75 | 0.87 | 0.06 | asserted 0.99 |
| s6 | Finally, we provide a tractable implementation of this algorithm for the optimal control of L-smooth nonlinear dynamical systems. | contribution 0.88 | 0.92 | 0.15 | asserted 1.00 |
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Original abstract
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. Finally, we provide a tractable implementation of this algorithm for the optimal control of L-smooth nonlinear dynamical systems.
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In [ref] , the authors propose a reachable set-based RRT planning algorithm that provides a formal guarantee in the presence of bounded perturbations, does not take into account the optimal control problem and is limited to piecewise constant controllers.
Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems · Introduction · 0.84
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