A hybrid stochastic river environmental restoration modeling with discrete and costly observations

• Published in: Optimal control applications & methods 2020-11, Vol.41 (6), p.1964-1994
• Main Authors: Yoshioka, Hidekazu, Tsujimura, Motoh, Hamagami, Kunihiko, Yoshioka, Yumi
• Format: Article
• Language: English
• Subjects: Algorithms; discrete and costly observation; Environment models; Environmental restoration; hybrid system; Optimal control; Optimization; Parabolic differential equations; Parameter identification; Partial differential equations; Restoration; river restoration; stochastic impulse control under partial information; Stochastic processes; Uncertainty
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2616

Summary A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This setting harmonizes with real problems because continuously obtaining environmental and ecological information is difficult, and is often costly. The main problem is to decide when and how much of the sediment should be supplied into a river environment to effectively suppress bloom of benthic algae. The interventions are allowed only at observation times. Finding the optimal river restoration policy ultimately reduces to solving an optimality equation in an unconventional form due to the observation cost and discrete observations. We show its unique solvability and present a connection with degenerate parabolic partial differential equations, with which we can construct an effective algorithm for its approximation. An uncertainty‐averse optimization problem is also considered as an advanced problem. Coefficients and parameter values are identified from experimental and observation results to numerically compute the optimal restoration policy of an existing river environment with and without uncertainty.