Linear complementarity model predictive control with limited iterations for box-constrained problems

This paper presents a sufficient condition and its certification algorithm for solving box-constrained linear model predictive control (MPC) problems within a certain number of iterations equal to the number of constrained prediction points. For implementing a model predictive controller in industrial applications, it is crucial to guarantee a concrete upper bound on the computational load so that the processor specifications can be determined. To address this matter, we transform the constrained quadratic optimization of MPC into an equivalent linear complementarity problem (LCP). Then, we show that if a modified n-step vector exists for a given problem, the corresponding LCP is feasible and solvable within a predetermined number of iterations, each comprising fundamental arithmetic operations. The existence of a modified n-step vector is independent of the current states and box constraint bounds. Thus, the total computational load required to solve an MPC problem can be explicitly determined. In addition, an explicit certification algorithm for checking the existence of a modified n-step vector is proposed. Utilizing this algorithm, the existence range of a modified n-step vector is investigated for various problem configurations. Numerical tests show that the computational speed of the proposed method is competitive with those of commonly available algorithms.