Model predictive control based on linear programming - The explicit solution
Model predictive control based on linear programming - The explicit solution
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DOI：
10.1109/tac.2002.805688
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发表时间：
2002-12-01
影响因子：
6.8
通讯作者：
Morari, M
中科院分区：
文献类型：
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作者：
Bemporad, A;Borrelli, F;Morari, M
我们研究具有输入和状态约束的离散时间线性时不变系统的模型预测控制（MPC）方案，可以使用线性程序（LP）来制定。尤其;我们将注意力集中在基于混合 1/无穷范数的性能标准上，即时间方面的 1 范数和空间方面的无穷范数。首先，我们提供一种计算终端权重的方法，以实现闭环稳定性。然后，我们证明最优控制曲线是初始状态的分段仿射连续函数，并简要描述计算它的算法。分段仿射形式允许消除在线 LP，因为与 MPC 相关的计算变成了简单的函数评估。除了实际优势之外，MPC 控制器的显式结构的可用性还提供了对状态空间不同区域中控制行为类型的洞察，并突出了 LP 简并的可能条件，例如多重最优。
We study model predictive control (MPC) schemes for discrete-time linear time-invariant systems with constraints on inputs and states, that can be formulated using a linear program (LP). In particular; we focus our attention on performance criteria based on a mixed 1/infinity-norm, namely, 1-norm with respect to time and infinity-norm with respect to space. First we provide a method to compute the terminal weight so that closed-loop stability is achieved. We then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it. The piecewise affine form allows to eliminate online LP, as the computation associated with MPC becomes a simple function evaluation. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.