scholarly journals Concepts of scattering in the linear optimal-control problem

1971 ◽  
Vol 118 (12) ◽  
pp. 1823 ◽  
Author(s):  
H. Nicholson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Linear Optimal Control

Optimal control of a hyperbolic system that describes Slutsky demand

2021 ◽  
pp. 58-59
Author(s):  
Olha Milchenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic System ◽  
Method Of Characteristics ◽  
Social Processes ◽  
Computational Algorithms ◽  
Initial Condition ◽  
Linear Optimal Control ◽  
First Order

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2400-2417 ◽  
Author(s):  
Ming-Yong Zhao ◽  
Xiao-Shan Gao ◽  
Qiang Zhang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Original Problem ◽  
Robotic Manipulators ◽  
Linear Optimal Control ◽  
Time Optimal ◽  
Optimal Trajectory Planning

SUMMARYThis paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound κ. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of κ = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.

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