输入受约束线性二次调节器的时长估计

Horizon Estimation for Input Constrained Linear Quadratic Regulator

对于含有输入约束的无限时长线性二次调节问题，为了将其转化为有限时长的模型预测控制问题，确定控制时长非常重要，如何快速得到保守性小的控制时长，目前还没有十分有效的算法。文章提出了一种估计控制时长的快速算法．计算零可控区域及其对应的顶点集，将初始状态投影到零可控区的某一个平面上，系统的初始状态可以表示成该平面上多边形顶点的凸组合，通过求解线性规划问题，得到性能指标的最小值，从而得到零可控区的控制时长的估计值。数值仿真结果表明所提出的算法具有较小的保守性，并且计算量小。

It is important to determine the control horizon for transforming the input constrained infinite horizon linear quadratic regulation problem into the finite horizon model predictive control problem. There isn＇t an efficient algorithm to get the small conservative control horizon quickly. A fast algorithm to estimate the control horizon is presented. The null controllable region and its vertex are computed and the initial state is projected into one facet of the null controllable region. The initial state is expressed as the convex combination of the vertexes. The minimal cost value can be obtained by solving a linear programming problem. The estimation of the control horizon can be computed quickly. From the numerical simulations, the new algorithm has the small conservation and computational complexity.