Data-Integrated-Embedded-Control

Course Project for ESE 559 Data-Integrated Frameworks for Systems Analysis and Control Design

Current topics of interest:

Efficient Triangulation

• Delaunay Triangulation is the standard, balanced triangulation algorithm
• Delaunay Triangulation can be calculated efficiently by projection on a convex hull
  • Ex. qhull.org
• Interested in efficiently altering triangulations when adding points over time

Delaunay Triangulation Over Time	Voronoi Graph Over Time

• Higher order Delaunay triangulations may also provide better modelling, similar to increasing k in KNN
  • Higher order Delaunay triangulations

Implications of taking samples from continuous time signals

Van der Pol Uniformly Sampled	Van der Pol Sampled Over Time

Clustering as a Nonlinearity Measure

• We can find simplex transformations (our method of linearizing the dynamics of a region between points)
• We can measure the similarity of these simplex transformations as a sort of non-linearity measure
  • Observability measures for nonlinear systems
• I also believe we can use simplex clustering to "cull" simplices in regions where the system is either very linear or has been oversampled

Balancing the ideas of memory and computational efficiency

• Simplex clustering and culling saves memory and makes region lookup faster
• Preserving the full grid of simplices makes Delaunay Triangulation quick and efficient
• How to balance or incorporate these two techniques to make real-time/offline modeling and learning efficient