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.

本文提出了一个充分的条件及其证明算法，可以在一定数量的迭代中（等于约束预测点的数量）解决盒约束线性模型预测控制（MPC）问题。为了在工业应用中实现模型预测控制器，至关重要的是要保证计算负载的具体上限，以便可以确定处理器规格。为了解决此问题，我们将MPC的约束二次优化转换为等效线性互补问题（LCP）。然后，我们表明，如果针对给定问题存在修改的n步向量，则相应的LCP在预定数量的迭代中是可行且可解决的，每个迭代都包含基本算术运算。修改后的n步向量的存在与当前状态和框约束范围无关。因此，可以明确确定解决MPC问题所需的总计算量。此外，提出了一种显式的证明算法，用于检查修改的n步向量的存在。利用该算法，针对各种问题配置，研究了修正的n阶向量的存在范围。数值试验表明，该方法的计算速度与常用算法相比具有竞争力。利用该算法，针对各种问题配置，研究了修正的n阶向量的存在范围。数值试验表明，该方法的计算速度与常用算法相比具有竞争力。利用该算法，研究了针对各种问题配置的修正n步向量的存在范围。数值试验表明，该方法的计算速度与常用算法相比具有竞争力。