On a new computing technique in optimal control and its application to minimal time flight profile optimization

1970 ◽  
pp. 1-20
Author(s):  
A. V. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Computing Technique ◽  
Minimal Time ◽  
Flight Profile ◽  
Profile Optimization

scholarly journals Dynamical modeling and optimal control of landfills

2016 ◽  
Vol 26 (05) ◽  
pp. 901-929 ◽  
Author(s):  
Alain Rapaport ◽  
Terence Bayen ◽  
Matthieu Sebbah ◽  
Andres Donoso-Bravo ◽  
Alfredo Torrico
Keyword(s):  
Optimal Control ◽  
Simple Model ◽  
Control Problem ◽  
State Space ◽  
Optimal Strategy ◽  
Dynamical Modeling ◽  
Minimal Time ◽  
Time Control ◽  
Switching Curve ◽  
Singular Arc

We propose a simple model of landfill and study a minimal time control problem where the re-circulation leachate is the manipulated variable. We propose a scheme to construct the optimal strategy by dividing the state space into three subsets [Formula: see text], [Formula: see text] and the complementary. On [Formula: see text] and [Formula: see text], the optimal control is constant until reaching target, while it can exhibit a singular arc outside these two subsets. Moreover, the singular arc could have a barrier. In this case, we prove the existence of a switching curve that passes through a point of prior saturation under the assumption that the set [Formula: see text] intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.

Aircraft configuration and flight profile optimization using simulated annealing

1999 ◽  
Vol 2 (4) ◽  
pp. 239-255 ◽  
Author(s):  
Rajkumar Pant ◽  
J.P. Fielding
Keyword(s):  
Simulated Annealing ◽  
Flight Profile ◽  
Profile Optimization

scholarly journals Minimal-time mean field games

2019 ◽  
Vol 29 (08) ◽  
pp. 1413-1464 ◽  
Author(s):  
Guilherme Mazanti ◽  
Filippo Santambrogio
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Value Function ◽  
Mean Field ◽  
Mean Field Games ◽  
Mean Field Game ◽  
Minimal Time ◽  
Regularity Properties ◽  
The Value Function

This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is bounded in terms of the average density of agents around their position in order to take into account congestion phenomena. After a preliminary study of the corresponding minimal-time optimal control problem, we formulate the mean field game in a Lagrangian setting and prove existence of Lagrangian equilibria using a fixed point strategy. We provide a further study of equilibria under the assumption that agents may leave the domain through the whole boundary, in which case equilibria are described through a system of a continuity equation on the distribution of agents coupled with a Hamilton–Jacobi equation on the value function of the optimal control problem solved by each agent. This is possible thanks to the semiconcavity of the value function, which follows from some further regularity properties of optimal trajectories obtained through Pontryagin Maximum Principle. Simulations illustrate the behavior of equilibria in some particular situations.

Modified bang‐bang controller for maximal and minimal time optimal control problems

2019 ◽  
Vol 22 (5) ◽  
pp. 1827-1839
Author(s):  
Kyung‐Tae Lee ◽  
Sang‐Young Oh ◽  
Ho‐Lim Choi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Minimal Time ◽  
Time Optimal

On a New Computing Technique in Optimal Control

1968 ◽  
Vol 6 (2) ◽  
pp. 149-173 ◽  
Author(s):  
A. V. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Computing Technique

A newton-type computing technique for optimal control problems

1984 ◽  
Vol 5 (2) ◽  
pp. 149-166 ◽  
Author(s):  
G. Di Pillo ◽  
L. Grippo ◽  
F. Lampariello
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Computing Technique

scholarly journals A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors

2020 ◽  
Vol 9 (2) ◽  
pp. 368-382
Author(s):  
Nahla Abdellatif ◽  
Walid Bouhafs ◽  
Jérôme Harmand ◽  
Frédéric Jean
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Sequencing Batch Reactor ◽  
Batch Reactor ◽  
The Other ◽  
Geometrical Approach ◽  
Minimal Time ◽  
Normative Constraints

In this work, we consider an optimal control problem of a biological sequencing batch reactor (SBR) for thetreatment of pollutants in wastewater. This model includes two biological reactions, one being aerobic while the other is anoxic. The objective is to find an optimal oxygen-injecting strategy to reach, in minimal time and in a minimal time/energy compromise, a target where the pollutants concentrations must fulfill normative constraints. Using a geometrical approach, we solve a more general optimal control problem and thanks to Pontryagin’s Maximum Principle, we explicitly give the complete optimal strategy.

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