Повышение эффективности детерминированных алгоритмов управления с использованием нейронных сетей /Enhancement of Deterministic Control Algorithms Using Neural Networks тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Кафа Висам

• Кафа Висам
• кандидат наук
• 2025

Оглавление диссертации кандидат наук Кафа Висам

Contents

Introduction

Chapter 1. Literature Review

1.1 Foundations of Model Predictive Control (MPC)

1.1.1 Principles and Receding Horizon Control

1.1.2 Mathematical Formulation of MPC

1.1.3 Strengths of MPC

1.1.4 Historical Milestones and Key Papers

1.2 Limitations of Traditional MPC

1.2.1 High Computational Demand

1.2.2 Sensitivity to Model Inaccuracy

1.2.3 Challenges with Time-Varying and Nonlinear Dynamics

1.2.4 Limitations in Handling Complex or Implicit Constraints

1.3 Neural Networks in Control Systems

1.3.1 Basics of Neural Networks (NNs)

1.3.2 Mathematical Background of NNs in Control

1.3.3 Role of NNs in Adaptive and Robust Control

1.4 Neural Network-Enhanced Model Predictive Control (NN-MPC)

1.4.1 Neural Networks for System Modeling in MPC

1.4.2 Neural Networks for MPC Optimization and Policy Approximation

1.4.3 Neural Networks for Robustness and Constraint Handling

1.5 Gaps in Literature and Motivation for This Research

1.5.1 What Existing Work Misses

1.5.2 Justification for Using FFNs and GRUs in This Research

Chapter 2. Methodology

2.1 Mathematical Modeling of the Gimbal System

2.2 Gimbal System Specifications

2.2.1 Motor and Rotor Parameters

2.2.2 Inertial Properties

2.2.3 Control Inputs and Disturbances

2.3 Robust Multi-Stage Nonlinear Model Predictive Control

2.4 Data Generation and Preprocessing

2.4.1 Equilibrium Point-Based Data Generation

2.4.2 Trajectory-Based Dataset Generation

2.4.3 Data Transformation and Temporal Structuring

2.4.4 Feature Engineering and Selection

2.5 Neural Network Training and Validation Strategy

2.5.1 Model Training Procedure

2.5.2 Model Testing and Evaluation Protocol

Chapter 3. Results and Analysis of Control Frameworks

3.1 Baseline: NMPC Controller Performance

3.1.1 Scenario Tree Visualization and Reference Tracking

3.1.2 Robustness to Disturbances

3.1.3 Effect of Prediction Horizon

3.1.4 Robustness to Noisy Measurements

3.1.5 Constraint Satisfaction Importance

3.1.6 Non-Zero Initial States

3.1.7 Computational Complexity and Solver Performance

3.2 Feedforward Neural Network (FNN)

3.2.1 Dataset Generation and Input Design

3.2.2 FNN-Based Learning Control under Fixed References

3.2.3 Dataset Design and Training Pipeline

3.2.4 FNN for Trajectory Tracking

3.2.4.1 Tracking Performance Evaluation

3.2.4.2 Disturbance Rejection Capabilities

3.2.4.3 Noise Resilience and Realistic Trajectory Testing

3.2.4.4 Model Mismatch Experiments

3.2.5 Summary Evaluation of the FNN-Based Controller

3.2.5.1 Qualitative Analysis of Model Behavior

3.2.5.2 Quantitative Results and Performance Metrics

3.2.5.3 Deployment Feasibility and Practical Implications

3.3 GRU Hybrid Approach Implementation

3.3.1 GRU Network Architecture

3.3.2 Training Pipeline

3.3.3 Inference and Real-Time Deployment

3.3.4 Results and Evaluation

3.3.5 Experimental Setup

3.3.6 Performance Metrics

3.3.7 Model mismatch and disturbance rejection

3.3.8 Comparative Summary

Conclusion

List of Abbreviations and Symbols

Glossary of Terms

Bibliography

List of Figures

List of Tables

Appendices

Введение диссертации (часть автореферата) на тему «Повышение эффективности детерминированных алгоритмов управления с использованием нейронных сетей /Enhancement of Deterministic Control Algorithms Using Neural Networks»

Introduction

Background and Motivation

Deterministic control algorithms are fundamental to modern control theory, providing structured methods for regulating systems where the future behavior can be predicted and controlled based on the current system state [16, 72]. These algorithms are widely used in various industries, such as aerospace, robotics, and process control, due to their ability to handle complex systems with multiple variables and constraints [25, 79]. Deterministic control refers to strategies where, given a specific set of initial conditions and inputs, the system's behavior can be predicted with certainty, and control actions can be determined in advance to achieve a desired output [64].

One well-known class of deterministic control algorithms is Linear Quadratic Regulator (LQR), which provides optimal control inputs by minimizing a cost function. LQR is effective for systems that are linear and operate within known constraints [16]. However, in more complex, nonlinear, or time-varying systems, LQR and similar methods can become insufficient, as they require accurate modeling of system dynamics and often lack flexibility in handling changes or disturbances [45, 59]. Moreover, while robust control methods can manage uncertainties and model inaccuracies, they are computationally expensive and not always well-suited to real-time applications [62, 65].

Model Predictive Control (MPC) has become a prominent solution to these limitations, offering flexibility and robustness for complex systems [30, 72]. MPC works by predicting the future behavior of a system over a fixed time horizon and then solving an optimization problem at each time step to determine the optimal control actions. The key advantage of MPC is its ability to handle multiple constraints (in inputs and outputs) and incorporate system dynamics into the optimization process [64]. However, despite its theoretical strengths, MPC comes with its own challenges, particularly in computational load and real-time performance. Each time step requires solving a complex optimization problem, which can be slow for systems with high dimensionality or complex constraints, leading to delays in decision-making [24, 38]. In systems where real-time control is critical, such as autonomous vehicles, drones, or manufacturing robots, this delay can lead to suboptimal control or even system instability.

Another significant issue is disturbances, which can impact the accuracy of predictions and the stability of control systems. MPC's reliance on an accurate model of the system means that it can struggle to handle unpredictable disturbances, such as external forces or changes in system dynamics [61, 65].

While techniques like robust MPC attempt to address this issue, they add complexity and increase computational demands, further complicating real-time applications [59].

The integration of neural networks into deterministic control algorithms, particularly MPC, offers a promising solution to these challenges. Neural networks excel in learning complex, nonlinear relationships from data and can adapt to changing system conditions without requiring explicit models [43, 47]. By training on historical data, neural networks can approximate system dynamics and predict future states with high accuracy, thus reducing the need for real-time optimization. This can dramatically reduce the computational burden of traditional MPC and improve control performance in dynamic environments [6, 33].

The integration of neural networks into model predictive control offers the potential to overcome many of the limitations of traditional approaches, particularly their heavy computational load and difficulties in real-time implementation [52, 58]. The central motivation of this research is therefore to strengthen deterministic control methods by introducing a new approach based on integrating specific neural network models into the MPC framework. In doing so, the study develops a hybrid strategy that improves computational efficiency, enhances adaptability, and increases robustness against disturbances, qualities that are crucial for demanding fields such as aerospace, robotics, and industrial process control.

Problem Statement

Model predictive control and related deterministic algorithms now play an important role in the regulation of complex and dynamic systems, particularly in areas such as aerospace, robotics, and industrial process automation [30, 72]. Despite their broad adoption and clear benefits, these methods also face a number of persistent difficulties that limit their wider application.

1. High Computational Demands: Traditional MPC requires solving an optimization problem at each time step, which can be computationally expensive, especially for systems with many variables and constraints [24, 65]. This computational burden becomes more problematic in realtime applications, where decisions need to be made quickly. The time required to compute optimal control inputs can lead to delays, reducing system performance or even causing instability in fast-moving or highly dynamic systems. For example, in robotics or Unmanned Aerial Vehicles (UAVs), even slight delays in control actions can result in poor tracking performance and loss of control [35, 36].

2. Handling of System Constraints: One of the key strengths of MPC is its ability to handle multiple constraints, such as limits on system inputs, states, and outputs [64, 72]. However, as the system complexity increases, the ability of traditional MPC to effectively manage these constraints

becomes more challenging. In many real-world applications, constraints are not only complex but also dynamic, changing over time or depending on external factors. Traditional MPC can struggle to handle these time-varying constraints efficiently, especially when the system operates in uncertain or unpredictable environments [59, 61].

3. Real-Time Adaptability: MPC is designed to optimize control over a finite time horizon, but it assumes a relatively static or predictable system model [45]. In many real-world applications, however, systems are subject to rapid changes in dynamics or external disturbances that make real-time adaptation critical. Traditional MPC algorithms can struggle to adapt to these changes quickly enough to maintain control, particularly in fast-paced or high-uncertainty scenarios [38, 52].

4. Disturbance Mitigation: Systems operating in dynamic environments often experience external disturbances (e.g., wind, temperature changes, sudden changes in load) that affect system behavior. While MPC can account for known disturbances by including them in the model, it often requires highly accurate system models to predict and mitigate their effects [62, 65]. In practice, however, these models can be imperfect, and disturbances may be unpredictable. Traditional MPC methods are limited in their ability to handle these unpredictable or unmodeled disturbances in real-time [32, 33].

In this dissertation, we consider several well-known shortcomings of deterministic control methods, and of model predictive control in particular. Among the most pressing are the excessive computational requirements that often prevent use in real-time settings; the difficulty of enforcing complex, time-dependent constraints; the limited ability to adapt quickly when system conditions change unexpectedly; and the dependence on highly accurate models, which reduces robustness to disturbances. The approach we propose here integrates specific designed neural networks models into the control framework with the aim of overcoming these problems, thereby improving efficiency, adaptability, and resilience in real-time operation [6, 43].

Research Objectives

Our primary objective in this research is to improve the performance and versatility of deterministic control algorithms, with particular emphasis on model predictive control, by integrating specifically designed neural networks into the control framework. Through this integration, we aim to address the main limitations of classical MPC, computational inefficiency, lack of adaptability in realtime settings, and limited robustness to disturbances, and, in doing so, extend its applicability to complex and dynamic systems.

To pursue this overarching goal, we formulated the following specific objectives:

1. Enhance Real-Time Control Performance.

We seek to reduce the computational burden of MPC's optimization procedure so that decisions can be made more quickly under stringent timing requirements. By training neural networks to approximate optimal control actions, we expect to achieve significant reductions in computation time, thereby making real-time control feasible even for high-dimensional systems. This objective will be evaluated through dedicated simulation studies measuring computation speed and performance.

2. Increase Robustness to Disturbances.

Another major goal is to design a control strategy that can better withstand external disturbances and model uncertainties. By training the suggested neural networks models on diverse datasets, we aim to develop a controller that responds effectively to perturbations without relying too heavily on exact system models. The improvements in robustness will be assessed by testing the system's response to a variety of disturbances in simulated and, where possible, experimental conditions.

3. Improve Adaptability to Dynamic Conditions.

Finally, we aim to enhance the adaptability of deterministic control algorithms in the face of rapidly changing dynamics and constraints. By leveraging the flexibility of suggested models, we intend to design controllers that can adjust smoothly to variations in real time, maintaining stability and performance under fluctuating operating conditions. This will be demonstrated through scenarios involving changes in system parameters and control constraints.

Taken together, these objectives guide our effort to develop a control framework that is not only more efficient, but also more robust and adaptable, qualities that are essential for deploying deterministic control methods in fast-changing, real-world environments.

Contributions of the Thesis

In this dissertation we develop a unique methodological framework for improving deterministic control algorithms, with a focus on Model Predictive Control. The originality of the work lies not in a single element but in the systematic combination of several newly designed methods that together enhance efficiency, robustness, and adaptability. The main contributions are as follows:

1. Method of Constrained Neural Approximations. We propose a new approach for constructing compact neural surrogates that approximate the optimization results of nonlinear MPC while

preserving system constraints. This method allows real-time decision making without sacrificing safety requirements.

2. Lightweight Hybrid Control Framework. We design a hybrid framework where Feedforward Neural Networks and Gated Recurrent Units reproduce the behavior of nonlinear MPC with significantly lower computational cost. This makes predictive control feasible for embedded and fast-response systems.

3. Trajectory-Oriented Training and Control. We introduce a training strategy that combines equilibrium-based and trajectory-based datasets with constraint-penalized loss functions and adaptive weighting. This procedure increases robustness to disturbances, improves generalization under model uncertainty, and ensures stable tracking in dynamic environments.

4. Unified Experimental Pipeline. We create a complete pipeline that covers system modeling, dataset generation, neural surrogate design, closed-loop integration, and comparative evaluation. This structured process ensures reproducibility and provides practical guidance for applying the developed methods in aerospace, robotics, and industrial systems.

Taken together, these contributions form a consistent framework that advances deterministic control methods beyond incremental improvements. The results demonstrate that predictive control can be made both efficient and reliable under real-time conditions, establishing a foundation for further research and for practical applications in complex technical systems.

Scientific Novelty

The novelty of our work lies in the development of new methods for integrating neural networks into deterministic control algorithms, in particular into nonlinear Model Predictive Control. The following elements reflect the new results:

1. A method of constrained neural approximations, which embeds safety requirements directly into the surrogate model and enables real-time decision making while preserving constraint satisfaction.

2. A lightweight hybrid control framework that combines feedforward and recurrent neural architectures, reproducing the behavior of nonlinear predictive control with a considerable reduction in computational cost.

3. A traj ectory-oriented training and control approach that unites equilibrium-based and traj ectory-based datasets with constraint-aware loss functions and adaptive weighting, thereby increasing robustness under disturbances and improving adaptability to dynamic conditions.

4. A structured experimental framework that links modeling, data generation, training, and closed-loop testing, providing a reproducible methodology for designing and validating neural surrogates in deterministic control tasks.

These results extend the theoretical basis of deterministic control by introducing new approaches to the systematic integration of neural networks into predictive algorithms.

Theoretical and Practical Significance

From a theoretical perspective, this research advances deterministic control by introducing new methods that systematically integrate neural networks into predictive algorithms. The method of constrained neural approximations extends the theory of surrogate modeling under constraints. The lightweight hybrid control framework and trajectory-oriented training approach contribute to the development of intelligent control techniques that combine model-based prediction with data-driven adaptability in nonlinear and uncertain conditions.

From a practical perspective, the proposed methods provide tools for creating controllers that are both fast and reliable. The developed framework reduces computational delays while preserving constraint satisfaction, making it suitable for real-time use in robotics, aerospace, and embedded platforms. The ability to balance efficiency, robustness, and adaptability broadens the range of technical systems where predictive control can be deployed.

Methodology and Research Methods

The research combines theoretical development, data-driven modeling, and computational experimentation within a unified methodological framework. The main stages are as follows:

• Mathematical modeling. A nonlinear dynamic model of a two-axis gimbal was developed as the test platform for the proposed methods.

• Data generation. A dedicated pipeline was created to produce both equilibrium-based and trajectory-based series datasets using nonlinear MPC simulations. This ensured that the training data reflected a wide range of operating conditions and disturbances.

• Neural network design and training. Compact FNN and GRU models were developed and trained using supervised learning. Specialized procedures were introduced, including constraint-

penalized loss functions and adaptive weighting, forming the basis of the trajectory-oriented training approach.

• Integration into the control loop. The trained neural models were embedded into the predictive control framework, creating a lightweight hybrid structure that preserved the advantages of MPC while reducing computational cost.

• Performance evaluation. The proposed controllers were benchmarked against conventional nonlinear MPC in closed-loop simulations. Evaluation criteria included accuracy, robustness under disturbances and uncertainties, constraint satisfaction, and computational efficiency.

All experiments were carried out on standardized computational platforms with reproducible settings, ensuring the consistency and reliability of results.

Propositions for Defense

The main propositions submitted for defense are:

1. The method of constrained neural approximations enables neural surrogates to reproduce the behavior of nonlinear MPC while satisfying real-time constraints and preserving system limitations.

2. The integration of specially designed neural components into deterministic control, including the trajectory-oriented training strategy and the hybrid FNN-GRU framework, increases robustness and adaptability under external disturbances, model uncertainties, and dynamically changing conditions.

3. The developed hybrid framework achieves a significant reduction in computational delays compared to conventional MPC, while maintaining comparable tracking accuracy and strict constraint satisfaction.

4. The structured methodology of this dissertation; covering modeling, dataset generation, neural training, and closed-loop evaluation; provides a reproducible process for applying neural surrogates in deterministic control tasks and demonstrates their practical feasibility.

Reliability and Approval of Results

The reliability of the results is ensured through multiple validation strategies, including:

• Simulation under a variety of disturbance and initial condition scenarios.

• Quantitative comparison with standard MPC performance benchmarks.

• Use of statistically robust performance metrics (e.g., tracking error, constraint violations,

computation time).

• External validation through presentation and discussion of intermediate results at academic

seminars and scientific conferences.

The results presented in this dissertation have been published in peer-reviewed journals and reflect original, independently verified work.

Compliance with the Specialty Passport

The dissertation is aligned with the passport of specialty 2.3.1 "System Analysis, Control and Data Processing, Statistics" and, in particular, with items P.1, P.2, P.3, P.4, P.5, P.9, P.10, P.11.

P.1-P.3. The work develops the theoretical and methodological foundations of systems analysis and control for a complex nonlinear technical object (a two-axis gimbal), formalizes optimal/predictive control tasks with state, input, and output constraints, and introduces criteria and models for evaluating effectiveness. The effectiveness criteria include tracking error, constraint-violation rate, computation time per control step, and robustness to parametric and disturbance uncertainty.

P.4-P.5. New methods and algorithms are proposed for solving constrained optimization and control problems under uncertainty: a hybrid nonlinear model predictive control scheme with neural surrogates (feedforward and gated recurrent networks) that approximate the NMPC law while preserving constraint handling. Specialized mathematical and algorithmic support is implemented in software to generate datasets, train surrogates, and integrate them into the predictive control loop.

P.9. The research is problem-oriented and targets the control, decision-making, and optimization of a real technical object. The complete pipeline, from modeling and identification to controller synthesis and benchmarking, addresses engineering requirements of closed-loop operation.

P.10. Intelligent decision-support methods are used to accelerate and stabilize the controller. Data-driven surrogates supplement model-based optimization, enabling fast on-board decision-making without sacrificing safety and constraint satisfaction.

P.11. Methods and metrics are developed for forecasting and assessing the quality, efficiency, and reliability of the closed-loop system. Comparative studies with baseline NMPC quantify performance across operating modes and disturbance scenarios, providing a grounded evaluation of the functioning of the complex control system and its components.

Approbation of the Results

The main results were presented and discussed at the 66th and 67th All-Russian Scientific Conferences of MIPT (Moscow, 2024-2025) and at the 8th International Conference on Information, Control, and Communication Technologies (ICCT-2024), with intermediate findings reported at seminars of the Laboratory of Digital Systems for Special Purposes (FRKT, MIPT); in addition, the results underwent approbation through publication in three peer-reviewed journals (Авиакосмическое приборостроение, Промышленные АСУ и контроллеры, Приборы и системы. Управление, контроль, диагностика, 2024-2025), one paper in international proceedings (ICCT-2024), one article submitted and under review, and one conference article.

Publications

The results of the dissertation are presented in three peer-reviewed journal articles, one paper in international proceedings, one article under review, two conference reports, one conference article accepted for publication. In Russian-language bibliographic records, the author's name appears as В. Кафа (Wissam Kafa). The full list is as follows.

Peer-reviewed journal articles (VAK/RSCI):

1. В. Кафа, Д.А. Гаврилов, В.Э. Буздин, Е.А. Татаринова, А.С. Фатеев, А.А. Меркелов, Д.С. Сичкарь, О.Ю. Зиновчик, О.А. Поткин. Робастная многоступенчатая нелинейная модель прогнозирующего управления для уменьшения помех в двухосной карданной системе. Авиакосмическое приборостроение, 2024, № 5, с. 17-36.

2. Кафа В., Гаврилов Д.А., Буздин В.Э., Татаринова Е.А., Фатеев А.С., Меркелов А.А., Сичкарь Д.С., Поткин О.А., Мурхиж Я. Недавние достижения в использовании нейронных сетей для повышения эффективности методов предиктивного управления. Промышленные АСУ и контроллеры, 2024, № 8, с. 20-35.

3. В. Кафа, Д.А. Гаврилов, Е.А. Татаринова, Я. Муридж, Н.Н. Щелкунов, Е.О. Савцов. Обучение моделей нелинейного предиктивного управления на основе данных: сравнение искусственных нейронных сетей и NMPC для управления нелинейными динамическими системами в реальном времени. Приборы и системы. Управление, контроль, диагностика, 2025, № 8, с. 1-11.

International proceedings (WoS/Scopus):

4. Y. Murhij, D. Gavrilov, V. Buzdin, W. Kafa, E. Tatarinova, A. Fateev, S. Shkatula, D. Krichevets. Visual Localization System for GPS-Blind Environments in Unmanned Aerial

Vehicles. In: Proc. of the 2024 8th International Conference on Information, Control, and Communication Technologies (ICCT), 2024, pp. 431-435.

Other publications and conference materials:

5. В. Кафа, Д.А. Гаврилов, В.Э. Буздин, Е.А. Татаринова. Real-Time Trajectory Tracking and Disturbance Mitigation via Feedforward Neural Approximation of NMPC Policies. Submitted, under review.

6. В. Кафа, Д.А. Гаврилов, В.Э. Буздин, Е.А. Татаринова, А.С. Фатеев, А.А. Меркелов. Робастная многоступенчатая нелинейная модель прогнозирующего управления для уменьшения помех в двухосной карданной системе. Доклад, 66-я Всероссийская научная конференция МФТИ, Москва, 2024.

7. В. Кафа, Д.А. Гаврилов, Я. Мурхиж, В.Э. Буздин, Е.А. Татаринова. Контроллер на основе нейронных сетей для замены NMPC в задачах отслеживания траектории в реальном времени и устранения помех. Доклад, 67-я Всероссийская научная конференция МФТИ, Москва, 2025.

8. А.С. Фатеев, Д.С. Сичкарь, В. Кафа. Аппаратно-программный комплекс визуальной системы локализации беспилотного транспортного средства. Статья, принята к публикации, 66-я Всероссийская научная конференция МФТИ, Москва, 2024.

Intellectual-property items:

9. Программное обеспечение контроллера двигателя. Свидетельство о государственной регистрации программы для ЭВМ № 2023686417, Роспатент, 06.12.2023. Соавторы: Д.А. Гаврилов, В. Кафа, А.А. Фортунатов и др.

10. Сложно-функциональный блок "локальный полиномиальный тонмаппер". Свидетельство о государственной регистрации программы для ЭВМ № 2024664557, Роспатент, 10.10.2024. Соавторы: В.Н. Чесноков, О.Ю. Зиновчик, В. Кафа и др.

11. Оптико-электронное устройство кругового обзора беспилотного транспортного средства. Патент на полезную модель № 235093, Роспатент, 20.06.2025. Соавторы: А.А. Меркелов, Е.А. Татаринова, В. Кафа и др.

Volume and Structure of the Work

The dissertation consists of an Introduction, 3 chapters, Conclusion, Bibliography, and appendices. The total volume is [120] pages, including [52] figures and [19] tables; the list of references contains [90] items.

Introduction. States the relevance, goals and objectives, scientific novelty, and theoretical/practical significance; outlines the methodology; formulates the propositions submitted for defense; and provides information on approbation, publications, and compliance with specialty 2.3.1.

Chapter 1: "Literature Review." Surveys deterministic control with emphasis on MPC (including robust and multi-stage formulations) and the integration of neural networks for control; identifies gaps that motivate the proposed approach.

Chapter 2: "Methodology." Describes the two-axis gimbal case study; dataset generation (static and trajectory-based); neural architectures (FFN, GRU, and hybrid FFN+GRU) for control-law approximation; integration of neural surrogates into NMPC; simulation platform and evaluation metrics.

Chapter 3: "Experimental Results." Presents baseline robust multi-stage NMPC performance; evaluates static and trajectory-based FFNs; implements GRU-based controllers; and compares accuracy, constraint handling, computation time, and robustness under disturbances and model uncertainty.

Conclusion. Summarizes the main results and contributions, discusses scientific and practical implications, and outlines directions for further research, including hardware implementation and online learning.

Appendices. Contain supporting materials.

Список литературы диссертационного исследования кандидат наук Кафа Висам, 2025 год

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