Data-Driven Optimal Control of Bilinear Systems

Abstract: This paper develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the system dynamics. Given an unknown bilinear system, we first characterize when the available data is suitable 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 data-based 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 convexify it and find a locally optimal control sequence. Simulations show that the performance of the proposed data-based approach is comparable with model-based methods.