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.

这项工作的重点是在随机环境中对可再生资源混合系统的最佳控制。我们提出一种新的配方，以通过收获和更新来处理最佳开采。随机环境由马尔可夫链建模，该马尔可夫链是隐藏的，只能在高斯白噪声中观察到。我们使用Wonham滤波器从可观察过程中估计马尔可夫链的状态。然后，我们在部分观察下建立了一个收获更新模型。马尔可夫链近似法用于找到价值函数和最优策略的数值近似。我们的工作考虑了实践中资源开发的自然方面：交互资源，切换环境，更新和部分观察。