Avtomatika i telemehanika

For linear multivariable continuous stationary stable control systems with a simple spectrum, presented in the form of a canonical diagonal form, controllability and observability forms, a method was developed and analytical formulas for spectral decompositions of gramians in the form of various Xiao matrices were obtained. A method and algorithm for calculatin  generalized Xiao matrices in the form of the Hadamard product for multiply connected continuous
linear systems with many inputs and many outputs have been developed. This allows us to calculate the elements of the corresponding controllability and observability gramians in the
form of products of the corresponding elements of the multiplier matrices and a matrix that is the sum of all possible products of the numerator matrices of the matrix transfer function of the system. New results are obtained in the form of spectral and singular decompositions of the inverse gramians of controllability and observability. This makes it possible to obtain invariant decompositions of energy functionals and formulate new criteria for the stability of linear systems taking into account the nonlinear effects of mode interaction.

Models and methods have been developed to verify the achievability of goals and the feasibility of plans implemented when managing large-scale systems in their development. An algorithm for analyzing the achievability of a set of goals and plans implemented when managing these systems is proposed and justified. Statements and hypotheses that make it possible to machine-check the feasibility of plans have been generated. A model example is given that confirms the possibility of checking the feasibility of plans for eliminating the consequences of a flood using the developed models and methods. In managing large-scale systems development, it is advisable to use control loops that check the achievability of set goals and the feasibility of plans over a selected time interval. In the absence of this verification, the chosen trajectory of development of a large-scale system at specific points in time may turn out to be unrealizable,
which will lead to disruption of the work being carried out, as well as to significant costs of the human, financial, technical and other types of resources for the implementation of obviously impracticable plans.

This paper is devoted to the blended (joint) finance mechanism of a megaproject consisting of several projects. One part of the megaproject budget comes from the megaproject manager and the other part from project contractors. When distributing this budget,
the megaproject manager considers information about the amount of the contractor’s internal funds allocated to project implementation. Project contractors seek to get more funds from the megaproject manager; in turn, the megaproject manager is interested in attracting more funds from project contractors. To achieve this goal, the megaproject manager applies different procedures to distribute the budget. Project contractors use the information reported to the
megaproject manager to increase the funds allocated to them. Straight and reverse priority distribution procedures in the blended finance mechanism are analyzed. A distribution procedure is determined that stimulates project contractors to allocate more of their internal funds to the project in a Nash equilibrium.

This paper proposes a method for diagnosing linear dynamic systems described by discrete-time models with exogenous disturbances based on interval observers. Formulas are derived to construct an interval observer producing two values of the residual as follows: if zero is between these values, then the system has no faults to be detected by the observer. The case where zero does not belong to the interval between these values is qualified as the occurrence
of a fault. The theoretical results are illustrated by an example.