Author:
Sigurdur Freyr Hafstein
Affiliation:
Reykajvik University, Iceland
Keyword(s):
CPA Function, Lyapunov Function, Piecewise Linear, Nonlinear System, Triangulation, Simplicial Complex, C++11, Armadillo Linear Algebra Library.
Related
Ontology
Subjects/Areas/Topics:
Computer Simulation Techniques
;
Dynamical Systems Models and Methods
;
Formal Methods
;
Mathematical Simulation
;
Non-Linear Systems
;
Simulation and Modeling
;
Simulation Tools and Platforms
Abstract:
Continuous, piecewise affine (CPA) functions can be algorithmically parameterized to deliver Lyapunov functions for compact invariant sets. We discuss flexible structures and algorithms to manipulate CPA functions for these purposes and discuss their implementation in C++11 using the Armadillo linear algebra library. Especially, we discuss some of the new language features in C++11 that lead to simpler and more readable code. The implementation was developed in the freeware Visual Studio Express 2012 for Windows Desktop (VS2012). Apart from a detailed description and code examples for the construction and manipulation of the simplicial complex that serves as a basis for CPA functions, this contribution includes some discussion on practical implementation details when using VS2012, C++11, and the linking to and use of the excellent Armadillo linear algebra library. Thus, some parts of this paper, especially Section 3, might be useful not only for those interested in the implementation
of the simplicial complex for computing CPA Lyapunov functions, but also for those generally interested in using the free Armadillo library for computations in VS2012.
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