scholarly journals On the construction of nearly time optimal continuous feedback laws around switching manifolds

2020 ◽  
Vol 26 ◽  
pp. 4
Author(s):  
Fabio Ancona ◽  
Cristopher Hermosilla
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimal Trajectories ◽  
Optimal Feedback ◽  
External Perturbations ◽  
Starting Point ◽  
Time Optimal ◽  
Continuous Feedback ◽  
Time Optimal Control Problem ◽  
Feedback Laws

In this paper, we address the question of the construction of a nearly time optimal feedback law for a minimum time optimal control problem, which is robust with respect to internal and external perturbations. For this purpose we take as starting point an optimal synthesis, which is a suitable collection of optimal trajectories. The construction we exhibit depends exclusively on the initial data obtained from the optimal feedback which is assumed to be known.

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 A minimal time optimal control for a drone landing problem

2021 ◽  
Author(s):  
Filippo Gazzola ◽  
Elsa Maria Marchini
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Aerospace Engineering ◽  
Time Optimal Control ◽  
Height Velocity ◽  
The Moon ◽  
Piecewise Constant ◽  
Time Optimal

We study a variant of the classical safe landing optimal control problem in aerospace engineering, introduced by Miele in 1962, where the target was to land a spacecraft on the moon by minimizing the consumption of fuel. A more modern model consists in replacing the spacecraft by a hybrid gas-electric drone. Assuming that the drone has a failure and that the thrust (representing the control) can act in both vertical directions, the new target is to land safely by minimizing time, no matter of what the consumption is. In dependence of the initial data (height, velocity, and fuel), we prove that the optimal control can be of four different kinds, all being piecewise constant. Our analysis covers all possible situations, including the nonexistence of a safe landing strategy due to the lack of fuel or for heights/velocities for which also a total braking is insufficient to stop the drone.

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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