A Decoupled Data Based Control (D2C) Approach to Generalized Motion Planning Problems

This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large partially observed Markov Decision Problem (POMDP). A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled "open loop-closed loop" fashion: first, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system, and then, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system which is learned using randomly perturbed input-output experimental data. Nonetheless, this decoupled approach can be shown to be near optimal. Computational examples are used to illustrate the performance of the proposed approach with a benchmark fully observed problem and a partially observed PDE control problem.