A parsimonious algorithm for the solution of continuous-time constrained LQR problems with guaranteed convergence

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance.