Tutorial by Prof. Florian Dorfler
Tutorial by Prof. Dong Eui Chang
Feedback integrators: A new method for structure-preserving numerical integration and controller design for dynamical systems on manifolds
October 29(Tue), 2024 14:00-17:00
Abstract: Structure-preserving numerical integration for ordinary differential equations is very crucial in numerical simulation of dynamical systems. In general, numerical integration of ordinary differential equations is expected to preserve first integrals and state-space manifolds such as energy, angular momentum and SO(3) for the free rigid body dynamics. As such, structure-preserving integration has been a vast research area for which various algorithms have been developed such as symplectic integrators, variational integrators and so on. Most of the algorithms, however, require special tricks, case-by-case, such as solving implicitly defined algebraic equations at each integration step or using a particular parameterization of a given manifold.
In this tutorial I will present a new method of structure-preserving integration, called feedback integrators, which does not require any of these special tricks but rather allows one to generally use any off-the-shelf numerical integrators such as the Euler method and the Runge-Kutta method, in order to numerically integrate a given dynamical system while preserving its conserved quantities. Feedback integrators apply to holonomic mechanical systems and non-holonomic mechanical systems as well as regular mechanical systems. They also extend to controller design for systems whose dynamics evolve on manifolds.
The main references for this tutorial are as follows:
● D.E. Chang, F. Jimenez and M. Perlmutter, “Feedback integrators,” J. Nonlinear Science, 26(6), 1693–1721, 2016.
● D.E. Chang and M. Perlmutter, “Feedback integrators for nonholonomic mechanical systems,” J. Nonlinear Science, 29, 1165-1204, 2019.
● D.E. Chang, “On controller design for systems on manifolds in Euclidean space,” International Journal of Robust and Nonlinear Control, 28 (16), 4981-4998, 2018.
● J.H. Park, S. Yoo and D.E. Chang, “A new paradigm for dealing with manifold structures in visual inertial odometry by using stable embedding,” IEEE Transactions on Control Systems Technology, 32 (3), 1098-1104, May 2024
