Data-Driven Optimal Control of Bilinear Systems

This letter develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the dynamics. Given an unknown bilinear system, we characterize when the available data is sufficiently informative to solve the optimal control problem. This characterization leads us to propose an online control experiment design procedure that guarantees that any input/state trajectory can be represented as a linear combination of collected input/state data matrices. Leveraging this representation, we transform the original optimal control problem into an equivalent data-based optimization problem with bilinear constraints. We solve the latter by iteratively employing a convex-concave procedure to find a locally optimal control sequence. Simulations show that the performance of the proposed data-based approach is comparable with model-based methods.