The maximum principle and the Hamilton-Jacobi-Bellman equation

2005 ◽  
pp. 111-121
Keyword(s):  
Maximum Principle ◽  
Bellman Equation ◽  
The Maximum Principle ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

Necessary and sufficient conditions for optimal controls in viscous flow problems

1994 ◽  
Vol 124 (2) ◽  
pp. 211-251 ◽  
Author(s):  
H. O. Fattorini ◽  
S. S. Sritharan
Keyword(s):  
Maximum Principle ◽  
Viscous Flow ◽  
Sufficient Conditions ◽  
Optimal Controls ◽  
The Maximum Principle ◽  
Flow Problems ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Necessary And Sufficient ◽  
The Pontryagin Maximum Principle

A class of optimal control problems in viscous flow is studied. Main results are the Pontryagin maximum principle and the verification theorem for the Hamilton–Jacobi–Bellman equation characterising the feedback problem. The maximum principle is established by two quite different methods.

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.

Viability-Based Computations of Solutions to the Hamilton-Jacobi-Bellman Equation

2007 ◽  
pp. 645-649 ◽  
Author(s):  
Alexandre M. Bayen ◽  
Christian Claudel ◽  
Patrick Saint-Pierre
Keyword(s):  
Bellman Equation ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman
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