We present and analyze a novel class of stabilizing and numerically efficient model predictive control (MPC) algorithms for discrete-time linear systems subject to polytopic input and state constraints. The proposed approach combines the previously presented concept of relaxed barrier function-based MPC with suitable warm-starting and sparsity-exploiting factorization techniques and allows to rigorously prove important stability and constraint satisfaction properties of the resulting closed-loop system independently of the number of performed Newton iterations. The effectiveness of the proposed approach is demonstrated by means of a numerical benchmark example.

中文翻译：

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用于模型预测控制的稀疏开发随时算法：一种宽松的屏障方法

我们提出并分析了一类新颖的稳定和数值有效的模型预测控制（MPC）算法，用于离散时间线性系统的多变量输入和状态约束。所提出的方法将先前提出的基于松弛势垒函数的MPC概念与合适的热启动和稀疏利用因子分解技术相结合，并能够严格证明所生成的闭环系统的重要稳定性和约束满足性，与所执行的次数无关牛顿迭代。通过一个数字基准示例证明了该方法的有效性。