论文标题
模型预测控制中的约束分离原理
A constraint-separation principle in model predictive control
论文作者
论文摘要
在此简介中，我们考虑了约束优化问题的基础模型预测控制（MPC）。我们表明，这个问题可以分解为与原始问题相同的成本函数的不受约束的优化问题，以及根据不受约束的问题的解决方案进行了改进的成本函数和动态的约束优化问题。在线性系统的情况下，不受限制的问题具有熟悉的LQR解决方案，而受约束的问题则减少到最小值投影。这意味着解决线性MPC问题等效于使用LQR预偿系统，并应用MPC仅惩罚控制输入。我们建议将其称为约束 - 分离原理，并讨论MPC方案设计中约束分离和一般分解的实用性，以及用于MPC问题的数值求解器的开发。
In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original problem and a constrained optimization problem with a modified cost function and dynamics that have been precompensated according to the solution of the unconstrained problem. In the case of linear systems subject to a quadratic cost, the unconstrained problem has the familiar LQR solution and the constrained problem reduces to a minimum-norm projection. This implies that solving linear MPC problems is equivalent to precompensating a system using LQR and applying MPC to penalize only the control input. We propose to call this a constraint-separation principle and discuss the utility of both constraint separation and general decomposition in the design of MPC schemes and the development of numerical solvers for MPC problems.
