PhD defence: Numerical method and application of optimal control problem

PhD defence of X. Liu MSc

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Summary

Pontryagin’s maximum principle, which provided the necessary condition for optimal control problems, results in two-point boundary problem. One numerical method that is easy to employ for such problems is the so-called  ”forward-backward  sweep” method. However this method is not always convergent especially when applied to non-linear systems.

In this thesis, firstly, we extend the “regularised forward-backward sweep iteration method” from the continuous setting to the discrete setting for solving optimal control problems. The continuous problem is discretized by using a variational integrator which yields a symplectic method.

Then we try to apply this method to Cucker-Smale model when the group of agents do not attempt to synchronize into uniform motion. In this problem, it is interesting to consider 'sparse control '', in which steering by the external controller is limited to a small number of finite actions.

In the end, the "regularised forward-backward sweep method" is applied into data assimilation. We proposed a new data assimilation algorithm, to utilizes the probability distribution of an esmble of controlled particles to quantify uncertainty in stochastic systems. Most importantly, the controlled dynamical system for the particles is deterministic. In the end, the method is defined as an optimal control problem. The cost function is composed of the norm of the control function and the Wasserstein distance on the observation space.

Start date and time
End date and time
Location
Academiegebouw, Domplein 29 & online (link)
PhD candidate
X. Liu MSc
Dissertation
Numerical method and application of optimal control problem
PhD supervisor(s)
prof. dr. ir. J.E. Frank