带不等式路径约束最优控制问题的惩罚函数法

A Penalty Method for Solving Inequality Path Constrained Optimal Control Problems

控制变量参数化(Control variable parameterization,CVP)方法是目前求解流程工业中最优操作问题的主流数值方法,但如果问题中包含路径约束,特别是不等式路径约束时,CVP方法则需要考虑专门的处理手段.为了克服该缺点,本文提出一种基于L1精确惩罚函数的方法,能够有效处理关于控制变量、状态变量、甚至控制变量/状态变量复杂耦合形式下的不等式路径约束.此外,为了能使用基于梯度的成熟优化算法,本文还引进了最新出现的光滑化技巧对非光滑的惩罚项进行磨光.最终得到了能高效处理不等式路径约束的改进型CVP架构,并给出相应数值算法.经典的带不等式路径约束最优控制问题上的测试结果及与国外文献报道的比较研究表明:本文所提出的改进型CVP架构及相应算法在精度和效率上兼有良好表现.

Control variable parameterization （CVP） method is currently popular for solving optimal control problems in process industries. However, dealing with path constraints is difficult in the framework of CVP method, especially for inequality path constraints. In order to conquer this flaw, this paper introduces the L1 exact penalty function from the mathematical programming into the field of optimal control so as to incorporate all the inequality path constraints into the original objective function. Besides, in order to use sophisticated gradient-based optimization algorithms, a novel smoothing technique is introduced to make the penalty terms differentiable. In this way, an enhanced CVP implementation structure which can handle inequality path constraints efficiently and a concomitant algorithm are proposed. Classic optimal control problems with path constraints are illustrated. Compared with the results by previous researchers, the results obtained in this paper demonstrate marked advantages in terms of accuracy and efficiency.