AI 中文总结
该研究针对无限视界稀疏最优控制问题，提出通过求解有限视界子问题结合后退视界技术实现的方法，保证了解的最优性与稀疏性，为无限视界稀疏控制提供了可行的求解途径。
AI 中文摘要
本文研究无限视界下的稀疏最优控制问题。现有文献中，稀疏控制多在有限视界下研究，因其可将问题转化为有限维优化问题。本文证明，无限视界稀疏控制问题的最优解可通过求解某一有限视界子问题得到，这是由于最优解具有稀疏性，即最优控制输入在尾部始终为零。本文给出该子问题所需视界长度的估计值，还讨论了其自适应选择方法。同时，本文考虑了采用后退视界技术的实现方式，该方式可保证最优性与稀疏性。
英文摘要
Sparse optimal control is considered in the infinite horizon. In the literature, sparse control has been considered mostly in a finite horizon for its formulation into a finite-dimensional optimization problem. It is shown in this paper that an optimal solution of the infinite-horizon sparse control problem can be obtained through a solution of some finite-horizon subproblem. This is due to sparsity of the optimal solution in the sense that the optimal control input is constantly equal to zero at its tail. An estimate is given on the horizon length required by this subproblem and its adaptive choice is also discussed. Implementation with a receding-horizon technique is considered and its optimality and sparsity are guaranteed.
Comments17 pages, 4 figures
