连续时间下的稀疏鲁棒最优控制：一种计算可行的方法
Sparse Robust Optimal Control in Continuous-Time: A Computationally Viable Approach
AI总结：
研究连续时间下的稀疏鲁棒最优控制问题，提出新算法框架，通过求解有限凸优化问题无损恢复原半无限规划的最优值与优化器，能解决相关系统问题，并经数值示例验证算法有效性。
AI中文摘要：
本文提出一种求解连续时间稀疏鲁棒最优控制问题的新的数值可行算法。考虑由常微分方程（ODE）控制的约束线性噪声系统，具有符合稀疏最优控制文献的\(L^1\)型目标函数。所得最优控制问题可采用半无限规划（SIP）公式。基于此，开发新框架可计算精确解，这在稀疏最优控制中尚属首次。证明可通过求解有限且计算可行的凸优化问题无损恢复原SIP的最优值和优化器，还能保证满足无数约束。还表明参数依赖噪声系统和最小关注问题可纳入框架并高效求解。通过基准数值示例展示了算法的有效性。
英文摘要：
This article presents a novel, numerically viable algorithm for solving sparse robust optimal control problems in continuous time. We consider a constrained linear noisy system governed by an ordinary differential equation (ODE), with an $L^1$-type objective function in line with the sparse optimal control literature. The resulting optimal control problem is shown to admit a semi-infinite programming (SIP) formulation. Building upon this insight, we develop a new framework that enables the computation of exact solutions -- to our knowledge, the first such achievement in the context of sparse optimal control. We demonstrate that a finite and computationally viable convex optimization problem can be solved to recover, in a lossless manner, both the optimal value and the corresponding optimizers of the original SIP, while also guaranteeing satisfaction of uncountably many constraints. We also show that the parameter-dependent noisy systems and the minimum attention problem fall into our framework and can be solved efficiently via our algorithm. The efficacy of our algorithm is illustrated through a benchmark numerical example.
