【作者】 张强； 李树荣； 张晓东； 雷阳；

【Author】 ZHANG Qiang,LI Shurong,ZHANG Xiaodong,LEI Yang College of Information and Control Engineering,China University of Petroleum(East China),Dongying 257061,P.R.China

【机构】 中国石油大学(华东)信息与控制工程学院；

【摘要】 基于约束凝聚和Pontryagin极大值原理,探讨了含状态和控制约束的最优控制数值解法.首先利用控制向量参数化(CVP)方法将原最优控制问题转化为静态的非线性规划问题.然后利用Kreisselmeier-Steinhauser(KS)函数将所有状态约束凝聚为一个终端时刻约束,通过求解伴随方程获得目标函数和约束的梯度.最后采用序列二次规划(SQP)方法获得问题的数值解.针对KS函数凝聚后的约束光滑性下降的问题,提出了一种自适应约束凝聚方法,在保证优化结果精度的前提下,有效减少了数值求解时间.仿真实例证明了方法的有效性.更多还原

【Abstract】 A numerical optimal control problem containing state and control constraints is discussed based on the constraint aggregation and Pontryagin maximal principle.First,a Control Vector Parameterization(CVP)method is used to convert the original optimal control problem into a nonlinear programming problem.Then,a Kreisselmeier-Steinhauser(KS)function is applied to lump all state constraints into a final time constraint,the gradients of object function and constraint are obtained by solving the adjoint equations.Finally,the numerical solution is obtained through Sequential Quadratic Programming(SQP) method.The smoothness of the constraint decreases after KS function aggregation,to this problem,a self-adaptive constraint aggregation method is presented.The method can effectivelydecrease numerical computation without reducing the optimization precision.Simulation examples demonstrate the effectiveness of this method.更多还原