Dynamic Optimization Problems and Applications

采用Stackelberg对策和激励策略的最新发展，提出了一种求解动态优化问题的新的分解方法。该方法涉及到阶段分解，并源于以下观察结果：在动态规划优化方法中，如果每个阶段的成本函数已知，则N阶段最优控制问题的解可以通过(并行)解N个解耦的静态(单阶段)优化问题来获得。以此为起点，主要调查人员建议，即使不知道最优成本函数，也可以从一些初始猜测开始，解决相应的N个静态优化问题，使用这些解更新初始猜测，解决一组新的优化问题，等等，直到达到一些收敛。研究了该算法的收敛性质、计算要求和可行性，并将其应用于电力系统中的经济调度问题。

Recent developments on Stackelberg Games and Incentive Strategies are adapted to develop a novel decomposition approach for the solution of dynamic optimization problems. The approach involves stage-wise decomposition, and stems from the following observation: "In the dynamic programming approach to optimization, if the cost-to-go functions at every stage were known, then the solution of an N-stage optimal control problem would be obtained by solving (in parallel) N decoupled static (single stage) optimization problems." Taking this observation as a starting point, the principal investigators suggest that even if the optimal cost-to-go functions are not known, one can start with some initial guesses, solve the corresponding N static optimization problems, update on the initial guesses using these solutions, solve a new set of optimization problems,...and so on..., until some convergence is achieved. The research is to study various aspects of this scheme, including its convergence properties, computational requirements, and feasibility, and apply it to an economic dispatch problem arising in power systems.