An iterative algorithm for constrained MPC with stability of bilinear systems

This paper presents a new algorithm for model predictive control (MPC) of constrained bilinear systems using iterative compensation of the prediction error and invariant sets for constraints satisfaction and stability guarantee. In order to improve the performance of the controller, which holds prediction as its essence, an iterative process is proposed with the objective of reducing the prediction errors due to the use of a quasi-linear approximation of the bilinear model. A study of the conditions under which the prediction error converges to zero is also provided. An important outcome of this property is that feasibility and effective state constraints satisfaction along the state trajectory can be achieved. For stability guarantee, a controlled-invariant set is computed and used as terminal constraint. Then, if the initial state is admissible, the state trajectory is assured to converge to this terminal set without violating the constraints. Once inside this region, a local controller can be used to drive the state to the operation point. Numerical examples illustrate the effectiveness of the proposed algorithm regarding convergence, constraints satisfaction and stability.