Gunther Reissig.

Approximate Value Iteration for a Class of Deterministic Optimal Control Problems with Infinite State and Input Alphabets.

Proc. 55nd IEEE Conf. Decision and Control (CDC),
Las Vegas, U.S.A.,
12-14 Dec. 2016, pp. 1063-1068.

Full text.
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**Abstract:**

We consider discrete-time deterministic optimal control problems in
which termination at some finite, but not predetermined nor a-priori
bounded time is mandatory. We characterize the value function as the
maximal fixed point of a suitable dynamic programming operator and
establish the convergence of both exact and approximate value
iteration under very general assumptions, which cover the classical
deterministic shortest path problem and its extension to hypergraphs
as well as reachability and minimum-time problems for sampled versions
of continuous control systems under constraints. In particular, the
state and input alphabets are infinite sets or metric spaces, and the
plant dynamics may be nonlinear and subject to disturbances and
constraints. The optimization is in the minimax (or maximin) sense,
the additive, extended real-valued running and terminal costs are
undiscounted and may be unbounded and of arbitrary signs, the value
function is typically discontinuous, and our results do apply to the
maximization of non-negative rewards under hard constraints.

**Erratum:**
Theorem V.1(ii) should read:
If $F$ is at most single-valued, then (11)
holds for all $p\; \in \; X$.

**BibTeX:**

@InProceedings{Reissig17DPc,
author = {Gunther Reissig},
title = {Approximate Value Iteration for a Class of Deterministic Optimal Control Problems with Infinite State and Input Alphabets},
booktitle = {Proc. IEEE Conf. Decision and Control (CDC), Las Vegas, U.S.A., 12-14 } # dec # { 2016},
pages = {1063-1068},
year = {2016},
address = {New York},
publisher = {IEEE},
doi = {10.1109/CDC.2016.7798408}
}

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