Information-State-Based Reinforcement Learning for the Control of Partially Observed Nonlinear Systems

This article develops a model-based reinforcement learning (RL) approach to the closed-loop control of nonlinear dynamical systems with a partial nonlinear observation model. We propose an "information-state"-based approach to rigorously transform the partially observed problem into a fully observed problem where the information state consists of the past several observations and control inputs. We further show the equivalence of the transformed and the initial partially observed optimal control problems and provide the conditions to solve for the deterministic optimal solution. We develop a data-based generalization of the iterative linear quadratic regulator (ILQR) for the RL of partially observed systems using a local linear time-varying model of the information-state dynamics approximated by an autoregressive-moving-average (ARMA) model that is generated using only the input-output data. This approach allows us to design a local perturbation feedback control law that provides an optimum solution to the partially observed feedback design problem locally. The efficacy of the developed method is shown by controlling complex high-dimensional nonlinear dynamical systems in the presence of model and sensing uncertainty.