Abstract: In chemical processes, there are constraints imposed on the inputs and outputs. For constraints on the outputs, which are not hard, i.e., the constraints can be violated to some extent, we can use fuzzy membership functions to describe the violation. However, in general, the fuzzy model predictive control problem is hard to be solved. Another method dealing with the violation of the output constraints is soft constraint method, i.e., allow the constraints on the outputs to be violated and then penalize the violation. For one kind of fuzzy model predictive control problems with specific membership functions and aggregation operators, we can transform it to a soft constraint optimization problem, which is basically a quadratic programming. Hence the computational burden is largely reduced. The simulation results verify the equivalence and the savings in the computational burden.

Key words: Model predictive control (MPC), soft constraint, fuzzy decision making, penalty function, piecewise linear

摘要： 在化工过程中，普遍存在着对输入输出以及状态变量的约束。针对干扰等因素导致预测控制没有可行解的问题，可以用设定模糊隶属度的方法描述“约束可以被一定限度的违反”，即将模糊决策引入到传统预测控制中。然而，模糊决策预测控制优化的求解通常较为复杂。另一种处理预测控制优化问题没有可行解的方法是软约束方法，即允许约束被违反并惩罚违反量。对于一类模糊决策预测控制优化问题的推导，可以通过设置相应的罚函数得到等价的软约束优化问题，从而将模糊优化问题转化为一个二次规划问题进行求解，简化了模糊决策预测控制的计算复杂程度。实验验证了该方法的正确性。

关键词: 预测控制, 模糊决策, 软约束, 罚函数, 分段线性