SOS-based stability region enlargement of bilinear power converters through model predictive control

Designing a controller for bilinear DC-DC boost converters which can guarantee safe and stable operation of the interconnected devices is always of major importance. In this paper, based on Sum of Squares (SOS) optimization, a controller is designed to guarantee Lyapunov stability for the closed-loop system. The optimization is formulated in order to achieve the largest possible Region of Attraction (ROA) for the considered equilibrium point while taking into account input and states constraints. The ROA and the Lyapunov function obtained with SOS are respectively taken as Terminal Set (TS) and Terminal Penalty (TP) of the Model Predictive Control (MPC). Compared to MPC without TS and TP, the use of these ingredients allows to guarantee stability in an enlarged ROA even with short prediction, thus limiting the computational complexity of the method. The proposed approach is demonstrated in simulation on a discrete-time bilinear model of a DC-DC boost converter. In order to account for the unmeasured states, a Kalman Filter is also used.