Multilevel optimal control of interconnected distributed parameter systems

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Abstract

In this paper, we have shown how the problem of the optimal control of interconnected distributed parameter systems using hierarchical control techniques can be tackled. The techniques given here enable one to obtain a collection of control sub-problems which retain their "distributed parameter" nature.

In this decomposition, it is necessary to choose a set of coordination variables which lead to an additive separable form for the Hamiltonian. Each of the sub-problems can be solved using the Maximum Principle. On the level of each sub-system, different types of criteria have been defined and these enable an optimal distribution of a collection of actuating points to be determined. In addition, it was considered necessary to include the study of a sub-system (control, controllability, application of actuators, and the dual problem of observation, observability and the implementation of sensors) taking into account the exchange of information between the different levels of the hierarchical structure.