Convex MPC With Unreachable Setpoint for a Class of Affine System

We propose a convex model predictive control (MPC) scheme for a class of affine input systems to reduce the dependence on terminal components and improve real-time control capability. Artificial reference variables are introduced to handle unreachable references, and the terminal set constraint is replaced with an equality constraint. Additionally, the original non-convex problem is replaced by a second-order-cone programming problem, while considering the linearization errors. A tube is constructed to ensure that the predicted states strictly satisfy the state constraints. Moreover, we identified two types of deadlock phenomena in this scheme: one caused by the non-convex characteristics, and the other caused by a zero radius tube. These deadlock are resolved by an adding constraints, and the proposed method is applied to the setpoint tracking problem of wheeled robots. By adjusting the corresponding parameters, a safety region, known as soft obstacle-avoidance constraint, is introduced to the state constraint, which differs from traditional constraint relaxation. Simulation results validate the effectiveness of the proposed method, and the influence of parameters on closed-loop trajectories is analyzed.