It is now well-known that many classes of deterministic control problems may be solved by max-plus or minplus (more generally, idempotent) numerical methods. These methods include max-plus basis-expansion approaches [1], [2], [7], [10], as well as the more recently developed curse-of-dimensionality-free methods [10], [15]. It has recently been discovered that idempotent methods are applicable to stochastic control and games. The methods are related to the above curse-of-dimensionality-free methods for deterministic control. In particular, a min-plus based method was found for stochastic control problems [11], [16], and a min-max method was discovered for games [12].
['Hidehiro Kaise', 'William M. McEneaney']
Idempotent expansions for continuous-time stochastic control: compact control space