论文标题
在收敛离散时间仿射系统的可触及值集上的二次最大化：可对角线的情况
Quadratic Maximization over the Reachable Values Set of a Convergent Discrete-time Affine System : The diagonalizable case
论文作者
论文摘要
在本文中，我们解决了一个最大化问题，其中目标函数是二次，凸或凹的，并且约束集是收敛离散时间仿射系统的可触及值集。此外，我们假设定义系统的矩阵是可对角线的。问题的困难在于无限顺序在约束集中处理。同等地，问题需要解决无限数量的二次程序。因此，主要思想是提取它们的有限，并确保提取问题的分辨率为初始问题提供了最佳值和最大化器。要解决的二次程序的数量必须是最小的。实际上，我们构建了一个整数家族，过分陈列于使用线性代数的基本思想来解决的二次程序数量。最终算法中使用了这个整数家族。算法中家庭整数的新计算确保了循环迭代次数的减少。本文中提出的方法在小的学术示例中进行了说明。最后，对算法进行了随机生成问题的实例。
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the matrix defining the system is diagonalizable. The difficulty of the problem lies in the infinite sequence to handle in the constraint set. Equivalently, the problem requires to solve an infinite number of quadratic programs. Therefore, the main idea is to extract a finite of them and to guarantee that the resolution of the extracted problems provides the optimal value and a maximizer for the initial problem. The number of quadratic programs to solve has to be the smallest possible. Actually, we construct a family of integers that over-approximate the exact number of quadratic programs to solve using basic ideas of linear algebra. This family of integers is used in the final algorithm. A new computation of an integer of the family within the algorithm ensures a reduction of the number of loop iterations. The method proposed in the paper is illustrated on small academic examples. Finally, the algorithm is experimented on randomly generated instances of the problem.
