Infimal Convolution and Optimal Time Control Problem III: Minimal Time Projection Set

2018 ◽  
Vol 28 (1) ◽  
pp. 30-44 ◽  
Author(s):  
Grigorii E. Ivanov ◽  
Lionel Thibault
Keyword(s):  
Control Problem ◽  
Optimal Time ◽  
Infimal Convolution ◽  
Minimal Time ◽  
Time Control ◽  
Minimal Time Projection ◽  
Time Projection

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.

scholarly journals Minimal time control of exact synchronization for parabolic systems

2021 ◽  
Author(s):  
Lijuan Wang ◽  
Qishu Yan
Keyword(s):  
Parabolic Systems ◽  
Optimal Time ◽  
Optimal Controls ◽  
Initial State ◽  
Solution Vector ◽  
Minimal Time ◽  
Time Control ◽  
System Of Parabolic Equations ◽  
Two Parameters ◽  
Necessary And Sufficient

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The purpose of such a problem is to find a control (from a constraint set) synchronizing components of the corresponding solution vector for the controlled system in the shortest time. In this paper, we build up a necessary and sufficient condition for the optimal time and the optimal control; we also obtain how the existence of optimal controls depends on the above mentioned two parameters.

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