Technological objects and processes are often characterized by fuzzy initial information necessary for developing their models and optimization. The purpose of the study is to develop a method for synthesizing linguistic models of fuzzy described objects and a heuristic method for solving the multicriteria optimization problem in a fuzzy environment. Based on the expert assessments and logical rules of conditional inference, a method for synthesizing linguistic models was developed for describing processes with fuzzy input and output parameters. To solve the problem of multicriteria optimization, a heuristic method based on the modification and combination of various optimality principles is proposed. Coking reactor models were developed by modifying the successive regression inclusion method and the least squares method. Linguistic models of the delayed coking process were developed in the Fuzzy Logic Toolbox, allowing to evaluate the coke quality depending on the temperature and pressure of coking reactors. Using the proposed heuristic method, the problem of two-criteria optimization of the delayed coking process with fuzzy constraints is solved. The results confirm the advantages of the proposed fuzzy approach compared with the well-known approaches. Unlike them, the proposed method allows making adequate decisions in a fuzzy environment by maximizing the use of available fuzzy information.

Multi-parametric industrial time-series forecasting is important for predictive monitoring, soft sensing, and decision support in complex process industries. This study proposes a process-informed hybrid ARX-residual deep sequence architecture for short-horizon multi-output forecasting of fluid catalytic cracking unit (FCCU) product yields. The model combines a frozen linear ARX branch with causal temporal convolution, a three-layer GRU, causal self-attention, additive attention pooling, residual gating, and a consistency-regularized multi-output objective. Experiments were performed on an open simulated FCCU benchmark containing 20,160 one-minute observations from seven normal and disturbed operating scenarios. The leakage-controlled pipeline uses scenario-wise chronological splitting, train-only median imputation and standardization, exclusion of fault-timing metadata and direct algebraic target components, and 30 min causal windows for five-minute-ahead forecasting. Across ten prespecified random seeds, the proposed model achieved a historical-test RMSE of 0.022809 $\pm$ 0.000116, compared with 0.022751 for ARX-like Ridge. Dependence-aware statistical analyses did not establish a consistent statistical advantage for either model across the evaluated runs. Rolling-origin evaluation likewise showed similar point accuracy, while leave-one-scenario-out evaluation revealed severe extrapolation failure for the unseen pressure-drop scenario. The results support the reproducibility of the proposed architecture and the importance of the ARX-based dynamic structure, but they do not establish the statistical superiority of the full deep residual architecture. Independent industrial data or newly prespecified simulation trajectories are required for confirmatory external validation.

The article addresses the problem of simultaneous estimation of states and parameters for a class of systems described by nonlinear ordinary differential equations, which model the operation of a counterflow heat exchanger. The augmented vector, which includes both states and parameters, is partially unobservable, and as shown by the analysis of global and local identifiability based on available experimental data, the estimation problem is ill-conditioned and requires regularization. For this purpose, a subset of estimable parameters was selected using an orthogonal method and a D-criterion optimization algorithm. Based on the experimental data, simultaneous estimation of states and parameters was performed using the UKF, with the set of estimated parameters including both the selected subset and competing parameter sets. Experimental-statistical modeling demonstrated that regularizing the estimation problem led to better results compared to non-optimal ones, and residual correlation analysis supports the conclusion of their reliability.

The paper studies the problems of developing fuzzy and linguistic models of poorly formalized production facilities using available fuzzy information and other types of data. Since known methods do not allow us to effectively solve these problems in a fuzzy environment, we propose a systematic method and a heuristic approach to decision making for the effective objects control in a fuzzy environment. The proposed system method makes it possible to develop fuzzy, linguistic models of complex objects, and a heuristic approach to the formulation and solution of the adoption problem - to adequately and effectively solve the problem of fuzzy described objects control. In the proposed heuristic method of fuzzy decision making, effective control of the coking process is ensured through the maximum and effective use of fuzzy information representing the experience, knowledge and intuition of the decision maker, experts. Using the proposed system method, fuzzy and linguistic models of the studied coking reactors of the delayed coking unit of the Atyrau refinery were developed. A computer modeling system has been created that allows, as a result of modeling, to select the optimal operating modes of coking reactors. Based on the developed models using the proposed heuristic decision-making method, modifying and combining the principles of maximin and Pareto optimality, the problem of effective control of the delayed coking process was successfully solved. Comparison of the obtained results with the results of known methods and real data shows the advantages, efficiency and high adequacy of the proposed methods in a fuzzy environment. The practical significance of the results obtained is that they can be adapted and successfully applied in modeling and decision making for the effective complex objects control in a fuzzy environment.

Фаза посадки во время полета, вероятно, является самой опасной частью, так как большинство аварий происходит на этой стадии. Для уменьшения влияния низковысотного сдвига ветра на продольное движение самолета в режиме посадки по глиссаде (заданию) предлагается робастное – управление. Построены динамические модели самолета и сдвиг ветра. Исследуются и методы синтеза для задачи управления полетом самолета в вертикальной плоскости при посадке в условиях неопределенных возмущений. Оба управления позволяют значительно уменьшить отклонение высоты. Однако, – субоптимальное управление обеспечивает лучшее качество переходных процессов как по высоте, так и по скорости, чем – оптимальное управление. Результаты моделирования синтезируемой системы подтверждают эффективность – управления для повышения робастной устойчивости к неопределенностям, вызванным возмущениями ветра.

The study presents a robust methodology for simultaneous state and parameter estimation in nonlinear thermal systems, demonstrated on a counter-current heat exchanger model operating with nitrogen under industrial conditions. To address challenges of ill-conditioning and parameter correlation, local sensitivity analysis is combined with regularization through optimal parameter subset selection using orthogonalization and D-optimal experimental design. The Unscented Kalman Filter (UKF) is employed to jointly estimate the augmented state vector in real time, leveraging high-fidelity dynamic simulations generated in Unisim Design with the Peng–Robinson equation of state. The proposed framework achieves high estimation accuracy and numerical stability, even under limited sensor availability and measurement noise. Monte Carlo simulations confirm robustness to ±2.5% uncertainty in initial conditions, while residual autocorrelation analysis validates estimator optimality. The approach provides a practical solution for real-time monitoring and model-based control in industrial heat exchangers and offers a generalizable strategy for building identifiable, noise-resilient models of complex nonlinear systems.