Stochastic control up to a hitting time: optimality and rolling-horizon implementation

Debasish Chatterjee; Eugenio Cinquemani; Giorgos Chaloulos; John Lygeros

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arXiv · 0806.3008

Stochastic control up to a hitting time: optimality and rolling-horizon implementation

Debasish Chatterjee·Eugenio Cinquemani·Giorgos Chaloulos·John Lygeros

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Abstract

We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact target set while simultaneously minimizing an expected discounted cost. We then provide a rolling-horizon strategy for approximating the optimal policy, together with quantitative characterization of its sub-optimality with respect to the optimal policy. Finally, we address related issues of asymptotic discount-optimality of the value-iteration policy. Both the state and action spaces are assumed to be Polish.

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Debasish Chatterjee, Eugenio Cinquemani, Giorgos Chaloulos, John Lygeros. 2009-09-28. Stochastic control up to a hitting time: optimality and rolling-horizon implementation. https://arxiv.org/abs/0806.3008

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