Optimal exploitation for hybrid systems of renewable resources under partial observation

This work focuses on optimal controls for hybrid systems of renewable resources in random environments. We propose a new formulation to treat the optimal exploitation with harvesting and renewing. The random environments are modeled by a Markov chain, which is hidden and can be observed only in a Gaussian white noise. We use the Wonham filter to estimate the state of the Markov chain from the observable process. Then we formulate a harvesting–renewing model under partial observation. The Markov chain approximation method is used to find a numerical approximation of the value function and optimal policies. Our work takes into account natural aspects of the resource exploitation in practice: interacting resources, switching environment, renewing and partial observation. Numerical examples are provided to demonstrate the results and explore new phenomena arising from new features in the proposed model.