Abstract:
The paper considers research of the plans stability of active moving objects (AMOs)
control system application. AMOs are material objects moving in space and carrying out
informational, material and energetic interaction with objects, control points and other AMOs.
Use of AMOs is usually regulated by strict requirements, so any time delay or incomplete
target effect are unacceptable. The reason of failing to perform a purpose task can be the
development of control using incorrect plans, so that realization of the plan is unstable due to
random factors or targeted effects of the environment and other systems. The paper deals with
problematic issues of complex research of active moving objects control application stability plans.
Quantitative and qualitative assessment methods of plans stability, ways and means of
ensuring required levels of stability are proposed by the authors. In this case planning task is
considered dynamic, which provides plan correction by means of organizational, structural and
program-algorithmic methods to ensure stability. The most adequate model of plan
implementation is appropriate system of differential equations. Notion of stability probability
is defined to account stochastic character of disturbance effect. The expression for stability
criterion is obtained. It allows to establish the fact of stability and unstability based on analysis
of properties of a purposefully built Lyapunov function and disturbances characteristics.
Developed technique of plans stability quantitative assessment is based on forecast of
possible amount of AMOs frustrated control procedures and additionally duration of process
control cycles. For solution of the problem of choosing stability rational ways, a flexible fuzzy
convolution is applied. It’s caused by the lack of additivity property of subjective experts
assessments. An example of multifunctional AMOs control points plans stability criterion is
provided. Quantitative assessments of stability plans in conditions of disturbance effects are
obtained. An example of defining priority of ways of stability provision is considered.
Keywords:stability across Lyapunov, stability on probability, Lyapunov's function, an active mobile object, the moment of the first exit, optimum control.