Symbolic Optimal Control
Symbolic Optimal Control
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DOI：
10.1109/tac.2018.2863178
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发表时间：
2017-09
影响因子：
6.8
通讯作者：
G. Reissig;M. Rungger
中科院分区：
文献类型：
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作者：
G. Reissig;M. Rungger
我们给出了一类非线性、连续状态、离散时间对象的极小极大意义下的最优控制问题的解的新结果。这类问题包括进入(退出)时间问题以及最短时间、追逐-逃避和到达-回避对策作为特例。我们利用辅助最优控制问题(“抽象”)来计算值函数的上界，即可实现的闭环系统性能的上界，以及实现这些上界的符号反馈控制器。抽象是通过离散化问题数据得到的，我们证明了当离散化参数趋于零时，符号控制器的计算界和性能收敛到值函数。特别地，如果最优控制问题在状态空间的某个紧子集上是可解的，并且离散化参数足够小，那么我们就得到了在该子集上求解该问题的符号反馈控制器。这些结果不假设值函数或任何问题数据的连续性，并且它们完全适用于存在硬状态和控制约束的情况。
We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state, discrete-time plants. The problem class includes entry-(exit-)time problems as well as minimum-time, pursuit-evasion, and reach-avoid games as special cases. We utilize auxiliary optimal control problems (“abstractions”) to compute both upper bounds of the value function, i.e., of the achievable closed-loop performance, and symbolic feedback controllers realizing those bounds. The abstractions are obtained from discretizing the problem data, and we prove that the computed bounds and the performance of the symbolic controllers converge to the value function as the discretization parameters approach zero. In particular, if the optimal control problem is solvable on some compact subset of the state space, and if the discretization parameters are sufficiently small, then we obtain a symbolic feedback controller solving the problem on that subset. These results do not assume the continuity of the value function or any problem data, and they fully apply in the presence of hard state and control constraints.