多时滞线性系统的控制参数优化方法

采用控制参数化方法研究具有连续状态不等式约束和多重状态及控制时滞的线性系统优化控制问题．通过把时滞系统动态模型中的控制量表示成关于时间的分段常数函数，把每个控制参数看作决策变量，将多时滞系统的控制问题转化为数学规划问题．推导出在连续状态不等式约束条件下的目标函数和约束函数对于待求参数的梯度公式，并用序列二次规划算法求出其最优控制量．最后，将该优化算法应用于湿法炼锌净化过程中．仿真结果表明，锌粉的添加量可以有效地减少，从而避免了资源的浪费．

Control parameterization method of linear systems with multiple time-delays

This paper studies the optimal control method using the control parameterization for a class of optimal control problems involving linear systems subject to continuous state inequality constraints where both the state and the control are allowed to have different time delays. The control of the dynamic system is approximated by a piecewise constant function whose magnitudes are taken as decision vectors. Then, formulae are derived for computing the gradients of the cost and constraint functions. On this basis, a computational method for finding the optimal control is obtained by using the sequential quadratic programming(SQP) algorithm. This computational method is applied to the purification process of zinc hydrometallurgy. The numerical simulation shows that the amount of zinc powder added can be decreased significantly so that the wastage of resources is avoided.