Real-time tunable approximated explicit MPC

Tunability is a major obstacle in the creation and subsequent application of the explicit model predictive control (MPC). The main bottleneck lies in the need to reconstruct the parametric solution each time weighting factors changes. Such an operation makes the implementation of the explicit MPC impractical. This manuscript addresses the problem of producing a suboptimal parametric solution to the optimal control problem, where the change of the weighting factor does not warrant the reconstruction of the explicit MPC. The solution is achieved by interpolating between two boundary explicit solutions for a range of values in weighing factors. Furthermore, we show that the suboptimal solution enforces the closed-loop stability and recursive feasibility. The stability and recursive feasibility are maintained by carefully choosing the terminal penalty and terminal set in those boundary explicit solutions.