Second-order conditions in a time-optimal control problem for linear system

2005 ◽  
pp. 368-376
Author(s):  
Nikolaj P. Osmolovskii
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Second Order ◽  
Order Conditions ◽  
Time Optimal Control ◽  
Second Order Conditions ◽  
Time Optimal ◽  
Time Optimal Control Problem

Solution of Finite-Time LQP Optimal Control Problems for Discrete-Time Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 151-157 ◽  
Author(s):  
M. J. Grimble ◽  
J. Fotakis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Time Optimal Control ◽  
Infinite Time ◽  
Time Problem ◽  
Z Domain ◽  
Time Optimal ◽  
Time Optimal Control Problem

The deterministic discrete-time optimal control problem for a finite optimization interval is considered. A solution is obtained in the z-domain by embedding the problem within a equivalent infinite time problem. The optimal controller is time-invariant and may be easily implemented. The controller is related to the solution of the usual infinite time optimal control problem due to Wiener. This new controller should be of value in self-tuning control laws where a finite interval controller is particularly important.

scholarly journals The Time-Optimal Control Problem of a Kind of Petrowsky System

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 311
Author(s):  
Dongsheng Luo ◽  
Wei Wei ◽  
Hongyong Deng ◽  
Yumei Liao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Null Controllability ◽  
Time Optimal Control ◽  
Necessary Condition ◽  
Vibration System ◽  
Time Optimal ◽  
Time Optimal Control Problem

In this paper, we consider the time-optimal control problem about a kind of Petrowsky system and its bang-bang property. To solve this problem, we first construct another control problem, whose null controllability is equivalent to the controllability of the time-optimal control problem of the Petrowsky system, and give the necessary condition for the null controllability. Then we show the existence of time-optimal control of the Petrowsky system through minimum sequences, for the null controllability of the constructed control problem is equivalent to the controllability of the time-optimal control of the Petrowsky system. At last, with the null controllability, we obtain the bang-bang property of the time-optimal control of the Petrowsky system by contradiction, moreover, we know the time-optimal control acts on one subset of the boundary of the vibration system.

scholarly journals A time optimal control problem for the collision-free robot motion planning

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 725-726
Author(s):  
Chantal Landry ◽  
Matthias Gerdts ◽  
René Henrion ◽  
Dietmar Hömberg
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Time Optimal Control ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Time Optimal ◽  
Time Optimal Control Problem
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