MPC for tracking piecewise constant references for constrained linear systems
MPC for tracking piecewise constant references for constrained linear systems
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DOI：
10.1016/j.automatica.2008.01.023
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发表时间：
2008-09
期刊：
影响因子：
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通讯作者：
D. Limón;I. Alvarado;T. Alamo;E. Camacho
中科院分区：
文献类型：
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作者：
D. Limón;I. Alvarado;T. Alamo;E. Camacho
针对约束（非平方）线性系统，提出了一种新的模型预测控制（MPC），用于跟踪分段常数参考。该控制器保证了约束满足和系统向任意可容许稳态目标的渐近演化。因此，任何分段允许的设定值序列都可以无误差地跟踪。如果目标稳态不允许，控制器将系统引导到最接近的允许稳态。这些目标是通过以下方式实现的：(i)添加人工稳态和输入作为决策变量；（ii）使用修改的成本函数来惩罚从人工稳态到目标稳态的距离；（iii）考虑基于不变量集概念的扩展终端约束进行跟踪。控制律是由一个对任何目标都可行的二次规划问题的解导出的。此外，所提出的控制器提供了比标准MPC更大的吸引力域（对于给定的控制范围），并且可以通过多参数编程工具显式计算。另一方面，增加到MPC的额外自由度可能会导致最优性的损失，这种损失可以通过补偿成本项的适当加权任意减少。
In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state. These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.