scholarly journals Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem

2016 ◽  
Vol 44 (10) ◽  
pp. 2922-2936 ◽  
Author(s):  
Friedl De Groote ◽  
Allison L. Kinney ◽  
Anil V. Rao ◽  
Benjamin J. Fregly
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Direct Collocation ◽  
Redundancy Problem ◽  
Problem Formulations

scholarly journals Time-Optimal Attitude Scheduling of a Spacecraft Equipped with Reaction Wheels

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Nonlinear Programming ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Mixed Integer ◽  
Optimal Sequence ◽  
Direct Collocation ◽  
Time Optimal ◽  
Binary Functions ◽  
Passage Times

The time-optimal control problem of a spacecraft equipped with reaction wheels has been studied, in which the spacecraft is constrained to sequentially assume a set of attitudes, whose order is not specified. This attitude scheduling problem has been solved as a multiphase mixed-integer optimal control problem in which binary functions have been introduced to model the choice of the optimal sequence of target attitudes and to enforce the constraint of adopting once and only once each attitude. Given the dynamic model of the spacecraft, the initial and final attitudes, and a set of target attitudes, solving this problem consists in finding the control inputs, the sequence of attitudes with the corresponding passage times, and the resulting trajectory of the spacecraft that minimize the time of the maneuver. The multiphase mixed-integer optimal control problem has been converted into a mixed-integer nonlinear programming problem first making the unknown passage times through the target attitudes part of the state, then introducing binary variables to discretize the binary functions, and finally applying a fifth-degree Gauss-Lobatto direct collocation method to tackle the dynamic constraints. The resulting problem has been solved using a nonlinear programming-based branch-and-bound algorithm.

scholarly journals GENERATION OF AN OPTIMAL LOW-ALTITUDE TRAJECTORY FOR A FIXED-WING UNMANNED AERIAL VEHICLE IN A MOUNTAINOUS AREA

Aviation ◽  
2021 ◽  
Vol 25 (2) ◽  
pp. 115-122
Author(s):  
Hossein Maghsoudi ◽  
Amirreza Kosari Kosari
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Three Dimensional ◽  
Direct Collocation ◽  
Aerial Vehicle ◽  
Low Altitude ◽  
Optimal Trajectory Planning

In this study, the three-dimensional optimal trajectory planning of an unmanned fixed-wing aerial vehicle was investigated for Terrain Following – Terrain Avoidance (TF-TA) purposes using the Direct Collocation method. For this purpose, firstly, the appropriate equations representing the translational movement of the aircraft were described. The three-dimensional optimal trajectory planning of the flying vehicle was formulated in the TF-TA manoeuvre as an optimal control problem. The terrain profile, as the main allowable height constraint was modelled using the Fractal Generation Method. The resulting optimal control problem was discretized by applying the Direct Collocation numerical technique and then, was transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method was demonstrated by extensive simulations, and it was particularly verified that the purposed approach can produce a solution satisfying almost all the performance and environmental constraints encountering in a low -altitude flight.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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