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基于多级表述策略,提出了二次求解具有控制切换结构动态优化问题的数值方法。基于常用的优化方法获得初始控制结构。动态优化问题根据控制结构进行分级,每一级对应一个特定的控制弧段,进而将原问题表述为一个多级动态优化问题。基于控制向量参数化(CVP),多级动态优化问题转化为一个非线性规划(NLP)问题进行求解。控制参数和级长作为优化变量。基于Pontryagin极大值原理,构造多级伴随系统,进而获得NLP求解器所需的梯度信息。仿真实例验证了方法的有效性。
Based on the multi-level representation strategy, a numerical method of solving the dynamic optimization problem with switching control structure is proposed. The initial control structure is obtained based on commonly used optimization methods. The dynamic optimization problem is graded according to the control structure. Each level corresponds to a specific control arc, and then the original problem is expressed as a multi-level dynamic optimization problem. Based on the control vector parameterization (CVP), the multi-level dynamic optimization problem is transformed into a non-linear programming (NLP) problem. Control parameters and level as optimization variables. Based on the Pontryagin maximum principle, a multistage adjoint system is constructed to obtain the gradient information required by the NLP solver. Simulation examples verify the effectiveness of the method.