Abstract
Optimal control problems for systems governed by partial differential equations are now solved currently. Restricting ourselves to open loop controls, the techniques used are essentially adaptations of those used for the control of lumped systems. Most successful of all is the gradient method although quasi Newton and conjugate gradient methods could be used ; however the selection of an efficient step size rule is more than ever crucial. The evaluation of the cost function is so expensive that the search for a one dimensional minimum must be avoided. Linear instantaneous constraints on the control and/or the states variables can be handled by the gradient projection method and/or duality or penalization.
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