Projection-Free Computation of Robust Controllable Sets with Constrained Zonotopes
แนวคิดหลัก
Efficiently compute inner- and outer-approximations of robust controllable sets using constrained zonotopes.
บทคัดย่อ
The content discusses the projection-free computation of robust controllable sets using constrained zonotopes. It proposes algorithms for inner- and outer-approximations, addressing numerical challenges in high-dimensional systems. The approach is demonstrated through case studies, emphasizing computational efficiency and scalability.
Directory:
Introduction
Definition of robust controllable sets.
Projection-Free Computation
Use of constrained zonotopes for approximations.
Data Extraction Algorithms
Closed-form expressions for key computations.
Inner-Approximation Algorithm
Steps to compute inner-approximations efficiently.
Outer-Approximation Algorithm
Procedure to obtain outer-approximations.
Sufficient Conditions for Exactness
Conditions under which the approximations are exact.
Implementation Considerations
Efficient computation strategies.
Projection-free computation of robust controllable sets with constrained zonotopes
สถิติ
Our approach can inner-approximate a 20-step robust controllable set for a 100-dimensional linear system in under 15 seconds on a standard computer.
คำพูด
"Unlike existing approaches, our approach does not rely on convex optimization solvers."
"Our approach can inner-approximate a 20-step robust controllable set for a 100-dimensional linear system in under 15 seconds."
How does the proposed method compare to traditional convex optimization-based approaches
The proposed method in the paper offers a projection-free approach to computing robust controllable sets using constrained zonotopes. This is a departure from traditional convex optimization-based approaches, which often rely on solving complex optimization problems to compute these sets. By avoiding the need for convex optimization solvers, the proposed method offers computational efficiency and scalability advantages. Additionally, the closed-form expressions provided by the proposed algorithms allow for faster computation of inner- and outer-approximations of robust controllable sets compared to traditional methods that involve iterative optimization processes.
What are the implications of assuming full dimensionality in the computations
Assuming full dimensionality in the computations has significant implications for the accuracy and feasibility of the results obtained. When working with full-dimensional constrained zonotopes, it ensures that certain operations such as computing an outer-approximating convex polyhedron or inner-approximating Pontryagin difference can be done accurately without losing information due to dimensionality reduction techniques like projections. Full dimensionality also allows for more precise representations of sets involved in set recursions, leading to more accurate approximations of robust controllable sets.
How might this research impact other fields beyond mathematics
The research presented in this paper on projection-free computation of robust controllable sets with constrained zonotopes has broader implications beyond mathematics. The efficient and scalable approach developed can have applications in various fields such as control systems engineering, robotics, aerospace technology, and autonomous vehicles. By providing tractable solutions for computing inner- and outer-approximate robust controllable sets under additive uncertainty constraints, this research can enhance decision-making processes in dynamic systems where uncertainties play a crucial role. The methodology could potentially lead to advancements in real-time control strategies for complex systems operating under uncertain conditions.
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Projection-Free Computation of Robust Controllable Sets with Constrained Zonotopes
Projection-free computation of robust controllable sets with constrained zonotopes
How does the proposed method compare to traditional convex optimization-based approaches
What are the implications of assuming full dimensionality in the computations
How might this research impact other fields beyond mathematics