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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December 2006
Technical Papers
Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application
Nhan Nguyen,
Nhan Nguyen
NASA Ames Research Center
, Mail Stop 269-1, Moffett Field, CA 94035
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Mark Ardema
Mark Ardema
Santa Clara University
, 500 El Camino Real, Santa Clara, CA 95053
Search for other works by this author on:
Nhan Nguyen
NASA Ames Research Center
, Mail Stop 269-1, Moffett Field, CA 94035
Mark Ardema
Santa Clara University
, 500 El Camino Real, Santa Clara, CA 95053J. Dyn. Sys., Meas., Control. Dec 2006, 128(4): 946-959 (14 pages)
Published Online: April 26, 2006
Article history
Received:
November 18, 2004
Revised:
April 26, 2006
Citation
Nguyen, N., and Ardema, M. (April 26, 2006). "Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application." ASME. J. Dyn. Sys., Meas., Control. December 2006; 128(4): 946–959. https://doi.org/10.1115/1.2362814
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