On the structure of the time-optimal controls for robotic manipulators

A technique for open-loop minimum time planning of time-histories of control torques for robotic manipulators subject to constraints on the control torques using evolutionary algorithm is presented here. Planning is carried out in joint space of the manipulator and the path is represented as a string of via-points connected by cubic spline polynomial functions. Repeated path modification is done by using the evolutionary algorithm to search for a time-optimal path. Time taken to traverse over a particular path is calculated by reducing the dynamic equations of motion over that path in terms of a path parameter and then calculating the time optimal-control over that path.

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On the local structure of time-optimal controls in R3

10.1109/cdc.1985.268590 ◽

1985 ◽

Cited By ~ 1

Author(s):

Heinz Schaettler

Keyword(s):

Local Structure ◽

Optimal Controls ◽

Time Optimal

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Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays

Mathematics ◽

10.3390/math9161956 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1956

Author(s):

Yong Han Kang ◽

Jin-Mun Jeong

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Functional Differential Equations ◽

Time Optimal Control ◽

Optimal Controls ◽

Stochastic Functional Differential Equations ◽

Time Optimal ◽

Target Set ◽

Functional Differential ◽

Stochastic Functional

The purpose of this paper is to find the time-optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is to construct a fundamental solution for corresponding linear systems and establish variations of a constant formula of solutions for given stochastic equations. The existence result of time-optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

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Free terminal time optimal control problem for the treatment of HIV infection

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2016.00270 ◽

2016 ◽

Vol 6 (1) ◽

pp. 33-51 ◽

Cited By ~ 2

Author(s):

Amine Hamdache ◽

Smahane Saadi ◽

Ilias Elmouki

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Hiv Infection ◽

Control Problem ◽

Time Optimal Control ◽

Optimal Controls ◽

Terminal Time ◽

Time Optimal ◽

Time Optimal Control Problem ◽

Free Terminal Time

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. The optimal treatment duration and the optimal medications amount are considered. The main objective of this study is to be able to maximize the benet based on number of healthy CD4+ T-cells and CTL immune cells and to minimize the infection level and the overall treatment cost while optimizing the duration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employedto provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.

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