W911NF-12-R-0012-03: Adaptive Integration of Nonsmooth Dynamical Systems
Abstract
The project seeks to produce accurate solutions of differential complementarity problems, used for simulating nonsmooth systems, through use of adaptive integration techniques. The proposal focused on using "guard functions", functions that yield a safe, generally conservative integration step size such that the trajectory of the system from t0 to t0+dt lies strictly within the admissible region for all unilateral constraints. Put another way we want to avoid integrating over nonsmooth events. By doing so, we can find intervals where the system trajectory is smooth. Then tools for smooth systems apply, e.g., higher order integration techniques, integration with error control. Major goals, as proposed originally, consist of: 1. Incorporating guard functions when unilateral constraints are strictly satisfied (i.e., g(x) = 0); in this case, the guard function will return zero, so a simulation would be unable to proceed using a purely guard function strategy (i. e., one could use the regula falsi numerical method to identify an integration step dt > 0 such that g(x(t0+dt)) >= 0, but the guarantee that system lies strictly within the admissible region over [t0, t0+dt] is lost). 2. Determining properties of good guard functions. The smaller the discrepancy between the "true" safe integration step size and that produced by the guard function, the faster a DCP can be solved. 3. Integration with error tolerances. This will allow DCPs to be solved- hopefully efficiently- to a desired level of accuracy 4. Benchmarks for verifiability. Since closed form solutions are not available for many nonsmooth systems, we seek to produce a set of benchmarks for testing the speed and accuracy of techniques for solving differential complementarity problems in our target application (multi-body dynamics simulation with hard contact).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1610118
Entities
People
- Evan Drumwright
Organizations
- Army Contracting Command
- George Washington University
- United States Army