Quantization of the Bellman equation, exponential asymptotics and tunneling

1992 ◽  
pp. 1-46 ◽  
Author(s):  
S. Dobrokhotov ◽  
V. Kolokoltsov ◽  
V. Maslov
Keyword(s):  
Bellman Equation ◽  
Exponential Asymptotics

scholarly journals On the terminal condition for the Bellman equation for dynamic optimization with an infinite horizon

2011 ◽  
Vol 24 (6) ◽  
pp. 943-949 ◽  
Author(s):  
Agnieszka Wiszniewska-Matyszkiel
Keyword(s):  
Dynamic Optimization ◽  
Bellman Equation ◽  
Infinite Horizon ◽  
Terminal Condition

scholarly journals Two-Phase Anisotropic Free Boundary Problems and Applications to the Bellman Equation in 2D

2017 ◽  
Vol 228 (2) ◽  
pp. 477-493 ◽  
Author(s):  
L. Caffarelli ◽  
D. De Silva ◽  
O. Savin
Keyword(s):  
Free Boundary ◽  
Bellman Equation ◽  
Free Boundary Problems ◽  
Two Phase ◽  
Boundary Problems

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.

The Hamiltonian–Jacobi–Bellman Equation for Time-Optimal Control

1989 ◽  
Vol 27 (6) ◽  
pp. 1477-1489 ◽  
Author(s):  
L. C. Evans ◽  
M. R. James
Keyword(s):  
Optimal Control ◽  
Bellman Equation ◽  
Time Optimal Control ◽  
Time Optimal
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