A stabilizing iteration scheme for model predictive control based on relaxed barrier functions
A stabilizing iteration scheme for model predictive control based on relaxed barrier functions
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DOI：
10.1016/j.automatica.2017.02.001
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Christian Feller;C. Ebenbauer
中科院分区：
文献类型：
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作者：
Christian Feller;C. Ebenbauer
我们提出并分析了一个稳定的迭代方案的算法实现的线性离散时间系统的模型预测控制多面体输入和状态约束。所需的在线优化利用一个宽松的障碍函数为基础的问题制定和执行两个连续的采样时刻之间的优化算法迭代的数量有限，可能很小。在稳定性分析中明确考虑了优化算法的动态特性以及所得到的控制输入的次优性，并证明了由状态和优化算法动态特性组成的整个闭环系统的起源是渐近稳定的。相应的约束满足特性也进行了分析。理论结果和数值算例表明，该算法的渐近稳定性和闭环性能与优化算法的迭代次数无关，从而得到一类新的稳定MPC算法.
We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems subject to polytopic input and state constraints. The required on-line optimization makes use of a relaxed barrier function based problem formulation and performs only a limited, possibly small, number of optimization algorithm iterations between two consecutive sampling instants. The optimization algorithm dynamics as well as the resulting suboptimality of the applied control input are taken into account explicitly in the stability analysis, and the origin of the resulting overall closed-loop system, consisting of state and optimization algorithm dynamics, is proven to be asymptotically stable. The corresponding constraint satisfaction properties are also analyzed. Both the theoretical results and a presented numerical example illustrate the fact that asymptotic stability as well as a satisfactory closed-loop performance may be achieved independently of the number of optimization algorithm iterations, thus leading to a novel class of stabilizing MPC algorithms.