Controller, second-integral three-state

The optimal control problem represents one of the most difficult optimization problems as it involves determination of optimal variables, which are vectors. There are three methods to solve these problems, namely, calculus of variation, which results in second-order differential equations, maximum principle, which adds adjoint variables and adjoint equations, and dynamic programming, which involves partial differential equations. For details of these methods, please refer to [23]. If we can discretize the whole system or use the model as a black box, then we can use NLP techniques. However, this results in discontinuous profiles. Since we need to manipulate the techno-socio-economic poHcy, we can consider the intermediate and integrated model for this purpose as it includes economics in the sustainabiHty models. As stated earlier, when we study the increase in per capita consumption, the system becomes unsustainable. Here we present the derivation of techno-socio-economic poHcies using optimal control appHed to the two models. 

The discussion in Section 6.14 showed that photochemical reactions can be divided into three main categories. First, there are reactions involving electron transfer. Second, there are reactions that take place on the excited-state surface and lead initially to excited products. Third, there are reactions that lead directly from excited reactants to products in their ground states, deexcitation occurring during the reaction and forming an integral part of it. In this section, we will consider this classification in detail and the factors that control the course of reactions of each type. 

In order to illustrate this issue, the paper considers an industrial controlled system on which a comparison study is performed. First the system failure is represented by a model that complies with the BDMP formalism. Second, the minimal cut sequences are extracted from this model. Section 2 describes the case study and gives the definition of the BDMP formalism. Section 3 applies the MBSA stated above while considering only the process failures. Then a control architecture is described, and added to the model in section 4. For integrating these new failures in the model, three models are proposed and discussed. In the same section, the set of minimal cut sequences is updated, and compared with the previous one. This comparison shows that the control failures have a significant influence on the qualitative analysis of the system. Finally, the last section draws up concluding remarks and outlooks. 

---