Second Variation Conditions for the Optimal Control Problem with Normalized Final Time

1994 ◽  
pp. 41-48
Author(s):  
David G. Hull ◽  
Christopher N. D’Souza
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Second Variation ◽  
Final Time

Minimum Energy Control Based on Vector Parameterization for Four-Wheel Drive Omni-Directional Mobile Robots

2013 ◽  
Vol 341-342 ◽  
pp. 784-790
Author(s):  
Jian Ping Chen ◽  
Jian Bin Wang ◽  
Yi Min Yang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Mobile Robots ◽  
Minimum Energy ◽  
Final Time ◽  
Wheel Drive ◽  
Time Optimal ◽  
Time Optimal Control Problem ◽  
Four Wheel Drive

Four-wheel drive omni-directional mobile robots (FDOMRs) usually carry limited energy and have to accomplish their tasks before deadlines. Energy saving can be achieved in several ways, and one of that is determining a velocity trajectory. To find the minimum energy trajectory, a practical cost function is chosen as the total energy drawn from the batteries. However, the cost function is a free final time optimal control problem, which is usually complex and has no explicit solution. A normalized time variable is used to transform the original problem into a fixed final time optimal control problem, which is solved by using uniform control vector parameterization. Various simulations are performed and the consumed energy is compared to the normal control method that without minimum energy consumption control. Simulation results show that the energy saving is much more compared to the traditional control, the operational time of the FDOMR with given batteries is lengthened and the efficiency of battery is improved.

scholarly journals Second variation of trajectory of a controlled dynamical system

2018 ◽  
Author(s):  
Oleg I. Drivotin
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Integral Representation ◽  
Control Problem ◽  
Order Method ◽  
Second Variation ◽  
The Third ◽  
The Second Variation

An integral representation for the second variation of trajectory of a dynamical system under control is obtained. This representation contains some tensor of the third rank introduced here. A differential equation for this tensor is presented. A second order method for solution of the optimal control problem based on the second variation of a trajectory is proposed.

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