- Series
- Dissertation Defense
- Time
- Monday, March 31, 2014 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jun Lu – School of Mathematics, Georgia Tech
- Organizer
- Jun Lu

This thesis proposes a novel and efficient method (Method of Evolving
Junctions)
for solving optimal control problems with path constraints, and whose
optimal
paths are separable. A path is separable if it is the concatenation of
finite
number of subarcs that are optimal and either entirely constraint active or
entirely constraint inactive. In the case when the subarcs can be computed
efficiently, the search for the optimal path boils down to determining the
junctions that connect those subarcs. In this way, the original infinite
dimensional problem of finding the entire path is converted into a finite
dimensional problem of determining the optimal junctions. The finite
dimensional
optimization problem is then solved by a recently developed global
optimization
strategy, intermittent diffusion. The idea is to add perturbations (noise)
to
the gradient flow intermittently, which essentially converts the ODE's
(gradient
descent) into a SDE's problem. It can be shown that the probability of
finding
the globally optimal path can be arbitrarily close to one. Comparing to
existing
methods, the method of evolving junctions is fundamentally faster and able
to
find the globally optimal path as well as a series of locally optimal
paths.
The efficiency of the algorithm will be demonstrated by solving path
planning
problems, more specifically, finding the optimal path in cluttered
environments
with static or dynamic obstacles.