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Nearly optimal simple explicit MPC controllers with stability and feasibility guarantees

机译：具有稳定性和可行性保证的近乎最佳的简单显式MPC控制器

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摘要

We consider the problem of synthesizing simple explicit model predictive control feedback laws that provide closed-loop stability and recursive satisfaction of state and input constraints. The approach is based on replacing a complex optimal feedback law by a simpler controller whose parameters are tuned, off-line, to minimize the reduction of the performance. The tuning consists of two steps. In the first step, we devise a simpler polyhedral partition by solving a parametric optimization problem. In the second step, we then optimize parameters of local affine feedbacks by minimizing the integrated squared error between the original controller and its simpler counterpart. We show that such a problem can be formulated as a convex optimization problem. Moreover, we illustrate that conditions of closed-loop stability and recursive satisfaction of constraints can be included as a set of linear constraints. Efficiency of the method is demonstrated on two examples. Copyright (C) 2014 John Wiley & Sons, Ltd.
机译：我们考虑了合成简单的显式模型预测控制反馈定律的问题，该定律提供闭环稳定性以及状态和输入约束的递归满足。该方法基于用更简单的控制器代替复杂的最佳反馈定律，该控制器的参数进行离线调整，以最大程度地降低性能降低。调整包括两个步骤。第一步，我们通过解决参数优化问题来设计一个更简单的多面体分区。在第二步中，我们然后通过最小化原始控制器与其较简单的控制器之间的积分平方误差来优化局部仿射反馈的参数。我们表明，这样的问题可以表述为凸优化问题。此外，我们说明了闭环稳定性和约束的递归满足条件可以包含为一组线性约束。在两个例子中证明了该方法的有效性。版权所有（C）2014 John Wiley＆Sons，Ltd.

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