Theory and applications of multivariable optimal periodic control



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This work is devoted to extensions of the theory of periodic processes and to applications of optimal periodic techniques to some biological processes. The theoretical investigations are mainly concerned with the systems described by functional differential equations. The necessary conditions for an optimal periodic process whose description involves constant as well as variable control and state delay have been derived first. Then, proper periodicity conditions have been developed via second variation analysis of the performance index. Systems described by ordinary differential equations with rational and product objective functionals have been considered as well. Proper periodicity criteria have been developed also for ordinary functionals and boundary-phase restricted controls. The examples from chemical engineering employed to illustrate the theory give rise to the conclusions that control phase relationship is a significant parameter which ought to be taken into account when designing multivariable periodic process. The state delay in a recycle process does not seem to be as nearly effective as control delay. [...]