Model Predictive Control of Bilinear Systems as Uncertain Linear Systems

In this paper, we develop a model predictive control (MPC) strategy for discrete-time bilinear systems by interpreting the bilinear model as a linear system with uncertainty in the state matrix. Using the fact that this uncertainty is restricted to a polytopic set, we apply the existing methodologies on robust MPC for linear systems to stabilize the bilinear system. Due to the interrelated nature of the polytopic uncertainty and the ability to control the system, which are both tied to the bounds on the input, a phenomenon emerges that the region of attraction under the MPC policy can be expanded by lowering the actuator bounds. We present an approach and discussion around maximizing this region of attraction by balancing the uncertainty and input strength. Numerical examples demonstrate the efficacy of the presented technique for both cases of single-input and multi-input bilinear systems.