Methods and algorithms for the synthesis of control systems for dynamic objects with partial observability

Abstract

The paper considers a class of dynamic technological objects operating under conditions of limited measurability of the state vector and the presence of stochastic disturbances. The problem arises from the fact that, in real industrial systems, available measurements represent projections of the system state onto the space of observable variables, which leads to uncertainty in the formation of control actions. Existing approaches based on the assumption of full observability or the use of reduced-order models do not provide the required accuracy and stability under transient conditions and variations in system parameters. The objective of the study is to develop methods for reconstructing latent components of the state vector and synthesizing control laws based on the processing of multidimensional time series generated during system operation. The theoretical framework is based on a state-space representation that explicitly accounts for measurement noise and external disturbances, as well as the introduction of estimated variables obtained through filtering and identification algorithms. The research tasks include the formalization of observability under incomplete data conditions, the development of state estimation algorithms, and the justification of the stability of the resulting closed-loop control system. The proposed approach is aimed at integrating information processing procedures and control synthesis into a unified mathematical framework that ensures consistency between state estimates and control actions. The practical significance lies in the applicability of the developed methods to problems in industrial process automation, where reliable system operation must be maintained under conditions of limited and noisy information support.