scholarly journals Optimal Control of Particle Advection in Couette and Poiseuille Flows

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Teresa Grilo ◽  
Fernando Lobo Pereira ◽  
Sílvio Gama
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Dynamic Control ◽  
Mathematical Framework ◽  
State Variable ◽  
Underwater Gliders ◽  
Time Control ◽  
The Pontryagin Maximum Principle ◽  
Couette And Poiseuille Flows ◽  
Poiseuille Flows

We present the problem of minimum time control of a particle advected in Couette and Poiseuille flows and solve it by using the Pontryagin maximum principle. This study is a first step of an effort aiming at the development of a mathematical framework for the control and optimization of dynamic control systems whose state variable is driven by interacting ODEs and PDEs which can be applied in the control of underwater gliders and mechanical fishes.

scholarly journals A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique

2003 ◽  
Vol 2003 (11) ◽  
pp. 631-650 ◽  
Author(s):  
Musa A. Mamedov
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Continuous Time ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Stationary Points ◽  
Control Problems ◽  
Horizon Problem ◽  
Time Control ◽  
Turnpike Theorem

We study the turnpike property for the nonconvex optimal control problems described by the differential inclusionx˙∈a(x). We study the infinite horizon problem of maximizing the functional∫0Tu(x(t))dtasTgrows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.

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