Aalborg Universitet Abstractions for Mechanical Systems

ions for Mechanical Systems Sloth, Christoffer; Wisniewski, Rafal Published in: Lagrangian and Hamiltonian Methods for Non Linear Control DOI (link to publication from Publisher): 10.3182/20120829-3-IT-4022.00049 Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link to publication from Aalborg University Citation for published version (APA): Sloth, C., & Wisniewski, R. (2012). Abstractions for Mechanical Systems. In Lagrangian and Hamiltonian Methods for Non Linear Control (1 ed., Vol. 4, pp. 96-101). Elsevier Science. (I F A C Workshop Series). DOI: 10.3182/20120829-3-IT-4022.00049 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research. ? You may not further distribute the material or use it for any profit-making activity or commercial gain ? You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from vbn.aau.dk on: september 01, 2017 Abstractions for Mechanical Systems ?ions for Mechanical Systems ? Christoffer Sloth ∗ Rafael Wisniewski ∗∗ ∗Department of Computer Science, Aalborg University, 9220 Aalborg East, Denmark (e-mail: [email protected]). ∗∗ Section of Automation & Control, Aalborg University, 9220 Aalborg East, Denmark (e-mail: [email protected]) Abstract: This paper proposes a method for discretizing the state space of mechanical systems. This is a first attempt in using reduction techniques for mechanical systems in the partitioning of the state space. The method relies on a combination of transversal and tangential manifolds for the conservative mechanical system. The tangential manifolds are generated using constants of motion, which can be derived from Noether’s theorem. The transversal manifolds are subsequently generated on a reduced space given by the Routhian, via action-angle coordinates. The method fully applies for integrable systems. We focus on a particular aspect of abstraction partitioning the state space, as existing methods can be applied on the discretized state space to obtain an automata-based model. The contribution of the paper is to show that well-known reduction methods can be used to generate abstract models, which can be used for formal verification. This paper proposes a method for discretizing the state space of mechanical systems. This is a first attempt in using reduction techniques for mechanical systems in the partitioning of the state space. The method relies on a combination of transversal and tangential manifolds for the conservative mechanical system. The tangential manifolds are generated using constants of motion, which can be derived from Noether’s theorem. The transversal manifolds are subsequently generated on a reduced space given by the Routhian, via action-angle coordinates. The method fully applies for integrable systems. We focus on a particular aspect of abstraction partitioning the state space, as existing methods can be applied on the discretized state space to obtain an automata-based model. The contribution of the paper is to show that well-known reduction methods can be used to generate abstract models, which can be used for formal verification.