Projection-Free Computation of Robust Controllable Sets with Constrained Zonotopes

核心概念

Efficiently compute inner- and outer-approximations of robust controllable sets using constrained zonotopes.

摘要

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.

統計資料

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.

引述

"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."

從以下內容提煉的關鍵洞見

Projection-free computation of robust controllable sets with constrained zonotopes

by Abraham P. V... 於 arxiv.org 03-21-2024

https://arxiv.org/pdf/2403.13730.pdf

深入探究

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.