  Many real-world systems often involve physical components or operating
environments with highly nonlinear and uncertain dynamics. A number of
different control algorithms can be used to design optimal controllers for such
systems, assuming a reasonably high-fidelity model of the actual system.
However, the assumptions made on the stochastic dynamics of the model when
designing the optimal controller may no longer be valid when the system is
deployed in the real-world. The problem addressed by this paper is the
following: Suppose we obtain an optimal trajectory by solving a control problem
in the training environment, how do we ensure that the real-world system
trajectory tracks this optimal trajectory with minimal amount of error in a
deployment environment. In other words, we want to learn how we can adapt an
optimal trained policy to distribution shifts in the environment. Distribution
shifts are problematic in safety-critical systems, where a trained policy may
lead to unsafe outcomes during deployment. We show that this problem can be
cast as a nonlinear optimization problem that could be solved using heuristic
method such as particle swarm optimization (PSO). However, if we instead
consider a convex relaxation of this problem, we can learn policies that track
the optimal trajectory with much better error performance, and faster
computation times. We demonstrate the efficacy of our approach on tracking an
optimal path using a Dubin's car model, and collision avoidance using both a
linear and nonlinear model for adaptive cruise control.
