SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 1077-1102, January 2020.
Optimal control problems with a very large time horizon can be tackled with the receding-horizon control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this article is the proof of the exponential convergence (with respect to the prediction horizon) of the control generated by the RHC method toward the exact solution of the problem. The result is established for a class of infinite-dimensional linear-quadratic optimal control problems with time-independent dynamics and integral cost. Such problems satisfy the turnpike property: the optimal trajectory remains most of the time very close to the solution to the associated static optimization problem. Specific terminal cost functions, derived from the Lagrange multiplier associated with the static optimization problem, are employed in the implementation of the RHC method.

中文翻译：

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线性二次最优控制问题的Turnpike特性和后退水平方法

SIAM控制与优化杂志，第58卷，第2期，第1077-1102页，2020年1月。
可以使用后退水平控制（RHC）方法解决具有很大时间范围的最优控制问题，该方法包括解决一系列具有较小预测范围的最优控制问题。本文的主要结果是证明由RHC方法生成的控制问题针对问题的精确解的指数收敛性（相对于预测范围）。建立了一类具有时间无关动力学和积分成本的无限维线性二次最优控制问题的结果。这样的问题满足了收费公路的特性：最优轨迹在大多数情况下都非常接近相关静态优化问题的解决方案。从与静态优化问题相关的拉格朗日乘数得出的特定终端成本函数，