Stochastic time-optimal control for time-fractional Ginzburg–Landau equation with mixed fractional Brownian motion

2021 ◽  
pp. 1-24
Author(s):  
Durga N ◽  
Muthukumar P ◽  
Xianlong Fu
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Landau Equation ◽  
Time Optimal Control ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Mixed Fractional Brownian Motion ◽  
Time Optimal ◽  
Stochastic Time

Safe Navigation With the Collision Avoidance of a Brownian Motion Obstacle

2017 ◽  
Author(s):  
Alexey A. Munishkin ◽  
Dejan Milutinović ◽  
David W. Casbeer
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Numerical Simulations ◽  
Collision Avoidance ◽  
Stochastic Optimal Control ◽  
Time Optimal Control ◽  
Value Functions ◽  
Point Location ◽  
Safe Navigation ◽  
Time Optimal

This paper develops a control that combines deterministic and stochastic optimal control solutions to the problem of safe navigation around a spherical obstacle in order to reach a way-point location. The solution for navigation towards the way-point is based on the deterministic minimum time optimal control. Since the intent of the obstacle is unknown to the navigating vehicle, the vehicle anticipates this uncertainty and uses a stochastic optimal control for navigation around the obstacle. The two navigation solutions are combined based on their value functions. Results are illustrated by numerical simulations.

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