Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Journal of Optimization Theory and Applications
Optimization by Vector Space Methods
Optimization by Vector Space Methods
The Convergence of Spectral and Finite Difference Methods for Initial-Boundary Value Problems
SIAM Journal on Scientific Computing
Representation and Control of Infinite Dimensional Systems (Systems & Control: Foundations & Applications)
On control design for PDEs with space-dependent diffusivity or time-dependent reactivity
Automatica (Journal of IFAC)
Mathematical and Computer Modelling: An International Journal
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Optimal control problems are formulated and solved in which the manipulation is distributed over a three-dimensional (3D) spatial field with constraints on the spatial variation. These spatial field control problems that arise in applications in acoustics, structures, epidemiology, cancer treatment, and tissue engineering have much higher controllability than boundary control problems, but have vastly higher degrees of freedom. Efficient algorithms are developed for computing optimal manipulated fields by combination of modal analysis and least-squares optimization over a basis function space. Small minimum control error is observed in applications to distributed parameter systems with reaction, diffusion, and convection.