Time Optimal Control of Balanced Manipulators

1989 ◽  
Vol 111 (2) ◽  
pp. 187-193 ◽  
Author(s):  
W. S. Newman ◽  
N. Hogan
Keyword(s):  
Optimal Control ◽  
Efficient Algorithm ◽  
Difficult Problem ◽  
Time Optimal Control ◽  
Restricted Class ◽  
Moving Targets ◽  
Problem Of Time ◽  
Time Optimal ◽  
On Line ◽  
Point To Point

An efficient algorithm is presented for solving time-optimal control for a restricted class of manipulators: balanced, decoupled manipulators. It is shown how the dynamics of such manipulators are sufficiently simple that optimal control solutions for point-to-point moves can be found analytically. A change of coordinates is proposed in which the more difficult problem of time-optimal interception of moving targets can be solved efficiently. A fast algorithm is described for computing and updating optimal interception solutions on line.

scholarly journals Two-channel time-optimal control of induction heating process with maximum temperature constraint

2020 ◽  
Vol 28 (2) ◽  
pp. 41-58
Author(s):  
Natalya A. Il`ina
Keyword(s):  
Optimal Control ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Time Optimal Control ◽  
Maximum Temperature ◽  
Heating Process ◽  
Problem Of Time ◽  
Control Actions ◽  
Time Optimal

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

scholarly journals Time-optimal control of fractional-order linear systems

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Optimal Control ◽  
Linear Systems ◽  
Control Function ◽  
Terminal State ◽  
Time Optimal Control ◽  
Fractional Dynamics ◽  
Support Functions ◽  
Problem Of Time ◽  
Time Optimal ◽  
Control Of Linear Systems

AbstractThe problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann- Liouville derivatives is considered. A method to construct a control function that brings trajectory of the system to the terminal state in the shortest time is proposed in terms of attainability sets and their support functions

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