Non-linear methods for decisions making processes under uncertainty conditions

The new methods of building strategies of imperfect inspections problems for successfully disclose of the disorder and the design of experiments with multi-alternatives are developed. Necessary and sufficient conditions are developed if the failure distribution is known explicitly, whereas a sufficient condition is given if only the increasing failure intensity is known from experiment.

Optimization algorithms of weakly controlled Markov renewal processes without discounting and the absorption state are constructed. An asymptotic behavior of a differential equation solution disturbed by a probability “cadlag” process is investigated. The existing and uniqueness of a global attractor for a probability dynamic system constructed on equation solutions when uniqueness condition is interrupted, that is, dynamic system is multi-valued, are proved. System analysis of individual and team decision problems in the format of an adaptive approach to multi-period decisions with information systems making more exact the nature state under stochastic uncertainty conditions had carried out. Optimal strategy of bounded quantity information sources allocation on Markov multi-period decision process is constructed. For two types controlled Markov processes (with the absorption state and the regular processes) conditions of optimal allocation of information sources on Markov multi-period decision process are received.

For controlled differential-operator equations, variational inequalities and evolution inclusions with non-linear, non-monotone, non-coercitive influence functions in common case the new features of multi-valued non-monotone mappings as uncertainty conditions are set up. The new constructive search methods of optimality equations for definition matrix coefficients of degenerate elliptic differential-operator equations and variational inequalities are established. For differential equations with partial derivatives and unknown parameters a priory estimates of convergences of high-exact algorithms for search approximate solutions are received, thus effect “blow-up” type is eliminated. In particular, an every solution of approximate countable system of ordinary differential equations is global, that is maximal existing time equal to + ∞