Gunther Reissig,
Matthias Rungger.
Symbolic Optimal Control.
IEEE Trans. Automat. Control, vol. 64, no. 6, June 2019, pp. 2224-2239.
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Abstract:
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.
BibTeX entry:
@article{ReissigRungger19,
AUTHOR = {Reissig, Gunther and Matthias Rungger},
TITLE = {Symbolic Optimal Control},
journal = {IEEE Trans. Automat. Control},
year = 2019,
volume = 64,
number = 6,
pages = {2224-2239},
month = jun,
doi ={10.1109/TAC.2018.2863178},
eprint = {1709.07333}
}
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