Optimal control of systems governed by time-delayed, second-order, linear, parabolic partial differential equations with a first boundary condition

1979 ◽  
Vol 29 (3) ◽  
pp. 437-481 ◽  
Author(s):  
K. L. Teo
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Order Linear

scholarly journals Modification of balayage spaces by transitions with application to coupling of PDE’s

2003 ◽  
Vol 169 ◽  
pp. 77-118 ◽  
Author(s):  
Wolfhard Hansen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential

AbstractModifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.

Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

2006 ◽  
Vol 128 (4) ◽  
pp. 946-959 ◽  
Author(s):  
Nhan Nguyen ◽  
Mark Ardema
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Control Problem ◽  
Boundary Control ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

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