A FUNCTIONAL-OPERATOR FRAMEWORK FOR THE EVOLUTION MODELING OF AUTONOMOUS MARITIME TECHNICAL SYSTEMS
DOI:
https://doi.org/10.35546/kntu2078-4481.2026.1.30Keywords:
autonomous marine technical systems; functional-operator approach; evolution equations; Hilbert space; strongly continuous semigroup; energy functional; spectral decomposition; stability of dynamic systems; mathematical modeling; risk-oriented managementAbstract
The article develops a functional-operator methodology for dynamic modeling of autonomous marine technical systems as distributed ergatic objects whose state evolves in Hilbert space. A mathematical apparatus is proposed, based on the formulation of the Cauchy problem for an abstract evolution equation with an operator matrix structure that takes into account the inertial, dissipative, and control components of the system. This formulation allows us to consider an autonomous marine technical device as a single multilevel system in which navigation, energy, information, and control processes are described within a common state space. The correctness of the problem is proved based on the theory of strongly continuous semigroups and conditions of maximum dissipativity of the operator, which guarantees the existence and uniqueness of a weak solution of the evolutionary equation. An energy functional is constructed, which provides analysis of the stability of the system and allows investigating its asymptotic behavior in the absence of external perturbations. The results obtained form the theoretical basis for interpreting the loss of system stability as a prerequisite for the emergence of dangerous modes of operation of autonomous marine platforms. A spectral decomposition of the operator was performed, which made it possible to move to a modal representation of the dynamics and establish a connection between the spectral structure of the system and multiscale modes of motion. It has been shown that the geometric properties of navigation trajectories recorded in AIS and ECDIS systems can be interpreted as a projection of the internal dynamics of an autonomous system, which opens up the possibility of using fractal-spectral characteristics as indicators of operating modes and the level of navigation risk. The results obtained form a universal mathematical framework for building intelligent decision support systems, risk-oriented management, and further integration of fractalspectral analysis in autonomous navigation tasks.
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