带时间延迟工业最优控制问题扩展控制变量参数化算法

Extended control variable parameterization approach for time-delay optimal control problems in industrial engineering

为了进一步提升控制变量参数化(CVP)算法在工程优化控制上的应用,提出一种求解带时间延迟最优控制问题的扩展CVP算法。该方法首先采用分段常量控制变量参数化和不等式路径约束光滑化处理技术将带时间延迟最优控制问题近似转化为非线性优化问题;定义辅助状态变量分析时间延迟状态变量扩展变分系统,并以此为基础推导目标函数和约束条件梯度信息;最后,针对两个典型工业过程时间延迟最优控制问题进行测试。结果显示,相较其他控制变量参数化直接法,提出方法能在更少优化参数下取得相近甚至更优的结果,表明所提出方法的有效性和正确性。

An extended control variable parameterization(CVP)approach for solving the time-delay optimal control problem was proposed to further promote the application of CVP method in industrial engineering.Firstly,the piecewise constant control parameterization and inequality path constraints smoothing handling technique were employed to transform the time-delay optimal control problem into an approximate nonlinear optimization problem.Then the auxiliary state variable was defined to analyse the extended variational system of time-delay state variables so as to obtain the gradient information of objective function and constraints.Finally,numerical tests were carried out on two typical time-delay optimal control problems in industrial engineering.Simulation results show that the proposed method is able to obtain similar or better solutions using fewer optimization parameters than other control parameterization direct algorithms,revealing the effectiveness and correctness of the proposed method.