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首页> 外文期刊>International Journal of Control >Constrained quadratic stabilization of discrete-time uncertain non-linear multi-model systems using piecewise affine state-feedback
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Constrained quadratic stabilization of discrete-time uncertain non-linear multi-model systems using piecewise affine state-feedback

机译：基于分段仿射状态反馈的离散时间不确定非线性多模型系统的约束二次镇定

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摘要

In this paper a method for non-linear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of thestate-space known as clusters the plant is assumed to be an element in a polytope whose vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to being linear systems. Theclusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a singlenon-convex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed loop. The feasibility problem is attacked by a branch-and-bound-based global approach. If the feasibility check is successful, the Lyapunov matrixand the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained non-linear model predictivecontrol is presented. In addition, the control design method is applied to a simple example.
机译：本文提出了一种基于双线性矩阵不等式（BMI）可行性问题的非线性鲁棒镇定方法。处理模型不确定性的稳健性。在状态空间的不同非重叠区域（称为簇）中，假定植物是其顶点（局部模型）是仿射系统的多面体中的元素。在封闭中包含原点的聚类中，局部模型仅限于线性系统。集群覆盖了国家空间中的关注区域。仿射状态反馈与每个群集关联。通过利用局部模型的亲和力和状态反馈，获得了一组线性矩阵不等式（LMI）与单个非凸BMI的组合，如果可行，可以保证闭环源的二次稳定性。可行性问题受到基于分支定界的全局方法的攻击。如果可行性检查成功，则通过可行解直接给出Lyapunov矩阵和分段仿射状态反馈。控制约束被表示为可以由LMI或BMI表示，并且提出了一种控制设计方法用于增强约束非线性模型预测控制的应用。另外，将控制设计方法应用于简单示例。

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