Extending the principle of minimum generalized work (Q1100424)

By using nonconventional functionals such as generalized work functionals in optimization, it is possible to solve the main present-day practical problem of optimal control, i.e., to generate real-time control signals of a complex linear system for achieving the principal objective of a given stage of operation of the system. A brief survey is presented of the development of the theory of the generalized work method, and the algorithm using a prediction model (PMA) is extended to the case of operator description of the system (model). Some procedures for diminishing the compute series (i.e. \(s_ N=\sum^{N}_{n=1}a_ n(1+s^{\alpha}_{n-1})^{-1}\), \(s_ 0=0\), where \(\sum a_ n\) is divergent). For the theorem see Bull. Inst. Math. Appl. 22, 66-70 (1986). (4) Values of \(\sum \mu (n)\) over various ranges. The results lead to the conjecture \[ Lim \sup (| \sum^{N}_{n=1}\mu (n)| (N \log \log N)^{-})=\sqrt{(12)/\pi} \] which implies the falsity of the Mertens Hypothesis (which is already known) and the truth of the Riemann Hypothesis (not yet known).