More efficient interpolating control

Recent papers proposed an interpolating control methodology for linear discrete-time systems subject to input and state (output) constraints. The main idea of the approach is to blend a local high-gain optimal controller with a global low-gain vertex controller via interpolation. At each time instant, two linear programming problems of relatively small dimensions are solved online. The approach can be seen as an alternative to optimization based control schemes such as model predictive control. However for high-dimensional systems, computing a feasible set for vertex control is generally challenging, and the ability to determine the feasible set limits the applicability of the approach. The aim of the present paper is to propose a way which removes this difficulty, yields further significant improvements on the computational complexity and on the degree of optimality.