Numerical Simulation of a Hamilton-Jacobi-Bellman Equation for Optimal Management Strategy of Released Plecoglossus Altivelis in River Systems

2016 ◽  
pp. 91-101 ◽  
Author(s):  
Yuta Yaegashi ◽  
Hidekazu Yoshioka ◽  
Koichi Unami ◽  
Masayuki Fujihara
Keyword(s):  
Numerical Simulation ◽  
Management Strategy ◽  
Bellman Equation ◽  
Optimal Management ◽  
River Systems ◽  
Plecoglossus Altivelis ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

OPTIMAL SHAPES OF WEIRS FOR TRAPPING MIGRATORY FISH

2016 ◽  
Vol 78 (1-2) ◽  
Author(s):  
Tadasuke Nakamichi ◽  
Koichi Unami ◽  
Masayuki Fujihara
Keyword(s):  
Bellman Equation ◽  
Lake Biwa ◽  
Mathematical Problem ◽  
Control Variable ◽  
Migratory Fish ◽  
Plecoglossus Altivelis ◽  
Optimal Shapes ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Traditional Fishing

Use of fishing weirs can be seen throughout the world to trap migratory fish in rivers. In rivers flowing into Lake Biwa, Shiga prefecture, Japan, a peculiar type of traditional fishing weir has been operated, targeting anadromous fish species such as Plecoglossus altivelis and Oncorhynchus masou rhodurus. That type of fishing weir has the advantage of catching fish alive, adding an extra value to the fish. Hence the structure of such a weir is considered to be historically optimized so that physiological damages to the fish are minimum. In this study, assuming that the horizontal shape is designed to minimize the traveling time of fish from any point along the downstream side of the weir to the gate of no return situated at the bank, as well as to minimize the size of structure, a mathematical problem is formulated in the framework of dynamic programming to determine the optimal shape. Geometric consideration results in the traveling time as a functional of the shape, whose slope of the tangent is dealt with as the control variable. The value function and the optimal control solve the Hamilton-Jacobi-Bellman equation, which represents the principle of optimality. The system of the Hamilton-Jacobi-Bellman equation is finally reduced to an ordinary differential equation with an initial condition. Some computational results are in good agreement with the actual shapes of the fishing weirs installed across the rivers flowing into Lake Biwa. This mathematical approach is also applicable to other problems such as optimal design of fish ladders.

Interception of automated adversarial drone swarms in partially observed environments

2021 ◽  
pp. 1-14
Author(s):  
Daniel Saranovic ◽  
Martin Pavlovski ◽  
William Power ◽  
Ivan Stojkovic ◽  
Zoran Obradovic
Keyword(s):  
Bellman Equation ◽  
Pid Controllers ◽  
Partially Observed ◽  
Hamilton Jacobi Bellman Equation ◽  
Partial Feedback ◽  
Point Solution ◽  
Physical Limitations ◽  
Defensive Mechanisms ◽  
Hamilton Jacobi Bellman ◽  
New Framework

As the prevalence of drones increases, understanding and preparing for possible adversarial uses of drones and drone swarms is of paramount importance. Correspondingly, developing defensive mechanisms in which swarms can be used to protect against adversarial Unmanned Aerial Vehicles (UAVs) is a problem that requires further attention. Prior work on intercepting UAVs relies mostly on utilizing additional sensors or uses the Hamilton-Jacobi-Bellman equation, for which strong conditions need to be met to guarantee the existence of a saddle-point solution. To that end, this work proposes a novel interception method that utilizes the swarm’s onboard PID controllers for setting the drones’ states during interception. The drone’s states are constrained only by their physical limitations, and only partial feedback of the adversarial drone’s positions is assumed. The new framework is evaluated in a virtual environment under different environmental and model settings, using random simulations of more than 165,000 swarm flights. For certain environmental settings, our results indicate that the interception performance of larger swarms under partial observation is comparable to that of a one-drone swarm under full observation of the adversarial drone.

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