Optimal Control System Research Articles

Data Visualization as a Means of Optimizing Control Systems Model in Project Management

The article addresses current issues concerning the utilization of data visualization in project management within the project context. It delves into the characteristics and principles of implementing projects within the project management framework of business entities. The classification of processes within the project management system is outlined. The study examines the significance of data visualization as a prerequisite for decision-making, highlighting the traits of visual project management. The tools employed for crafting visual representations of project data, derived from project implementation outcomes, are investigated. Various types of infographics intended for monitoring the execution of project-related business tasks, encompassing factors such as sequence, resources, and commencement and culmination dates, are identified. The article concludes by presenting the outcomes of generating visualizations using MS Project and MS Power BI within the realm of project management business processes in the project area.

Dynamic optimization of a wastewater treatment process for sustainable operation using multi-objective genetic algorithm and non-dominated sorting cuckoo search algorithm

Wastewater treatment plants (WWTP) face challenges due to nonlinearity and influent oscillations. An efficient optimal control system is necessary to improve effluent water quality without increasing operating costs. This research proposes a novel dynamic optimization control system using a non-dominated sorting-based multi-objective cuckoo search optimization algorithm (NSMOCS). Benchmark Simulation Model 1 (BSM1) was used as the WWTP model. Two sets of objectives were analyzed: the first set consists of the effluent quality index (EQI) and operating cost index (OCI), and the second comprises the reduction in nitrogen and ammonia concentrations at the WWTP. A Pareto front was obtained by evaluating these objectives using a multi-objective genetic algorithm (MOGA). Contribution analysis was used to find the individual weight values of these objectives. Furthermore, two sets of multi-objective cost functions were devised using weighted sum analysis. By minimizing the above-mentioned cost functions with NSMOCS algorithm, the best tuning parameters for the proportional integral (PI) controller were found. The simulation results with this proposed control strategy showed that the pollution units per day and the operating cost index were reduced during dry, rain, and storm weather conditions, with reductions of 1.3 %, 0.77 %, 0.91 %, and 0.9 %, 0.85 %, and 0.63 %, respectively.

Mengontruksi Kontrol Optimal Berkendala Pada Sistem LTI Dengan Keadaan Berkendala Menggunakan Metode Fungsi Penalti

The optimal control problem is defined as a problem in determining the control u(t) that depends on time t, such that it produces the optimum value for the objective function. The optimal control system with constrained conditions can be changed to an optimal control system without constraints by constructing the value of u(t) so that u(t) is not constrained. In this research, we will examine how to determine an optimal control of a system of time-independent state space or Linear Time Invariant (LTI) with constrained states and minimize a given objective function. In addition, how to construct an optimal controller that is constrained to become an optimal controller without constraints using the penalty function method and its implementation using Matlab. The results of this study are that the optimal control is:.

Singular fuzzy fractional quadratic regulator problem

This study aims to create a fuzzy optimal control system for a singular fuzzy fractional quadratic regulator problem, which is governed by singular fuzzy fractional differential equations. Additionally, this paper introduces new terms such as fuzzy stability, asymptotic stability, stabilizability, and detectability in the context of singular fractional control systems. Theoretical concepts regarding the stabilizability and detectability of these systems are also outlined, as well as a theorem and related algorithm for determining the fuzzy optimal control and trajectory of the singular fuzzy fractional quadratic regulator problem. The proposed method is tested through simulation on an electrical circuit modeled as a singular fuzzy fractional system, with results demonstrating the efficacy of the approach.

Digital-Twin-Based Coordinated Optimal Control for Steel Continuous Casting Process

A digital-twin-model-based optimal control system is presented for the steel continuous casting process. The system is designed for the coordinated optimization and dynamic control of secondary cooling and final electromagnetic stirring (FEMS), and involves three related parts. Firstly, a three dimensional real-time heat transfer model is established as the digital twin of the heat transfer process of continuous casting; for high accuracy, it is calibrated offline and calibrated online using measurements of the surface temperatures and shell thicknesses (only offline). Secondly, according to metallurgical rules, cooling and stirring are optimized coordinatively, based on the established digital-twin model and chaos particle swarm optimization algorithm. Thirdly, cooling and stirring are further dynamically controlled for quality stability. Finally, the system is applied in a bloom caster with model errors ≤ ±10 °C and control errors ≤ ±4 °C, which reduces the macro-segregation over grade 1.5 from 11% to 3.3%.

ДИНАМИЧЕСКАЯ МОДЕЛЬ АНАЛИЗА РИСКОВ ПРИ РЕАЛИЗАЦИИ СТРОИТЕЛЬНЫХ ПРОЕКТОВ НА ОСНОВЕ МАРКОВСКИХ СЛУЧАЙНЫХ ПРОЦЕССОВ

Accounting for possible risks that affect the successful implementation of construction projects is one of the most important tasks in planning and managing construction. The main problem for risk accounting is that they arise under the influence of random factors under conditions of high uncertainty. Therefore, the vast majority of risk accounting methods in construction are based on probabilistic models. Given the fact that recently the level of uncertainty in almost all areas of economic activity has increased significantly, it is necessary to develop new approaches to risk analysis that would respond as accurately and quickly as possible to emerging threats. Aim. The purpose of the study is to develop a mathematical model based on the theory of random Markov processes, which allows, in a probabilistic approach, to analyze the negative impact of adverse factors on the implementation of construction projects in the dynamics of their receipt under conditions of high uncertainty in order to increase the efficiency of construction work. Materials and methods. The risk assessment model of the influence of unfavorable factors on a construction project, presented in the paper, is based on the theory of Markov random processes, which makes it possible to assess the probability of the implementation of possible threats with varying degrees of damage, and to calculate risks during construction work. The model assumes that threats that cause different levels of damage to a construction project arrive at random times and require different times to eliminate them. To implement the model, a system of differential equations is given, which is solved by numerical methods. An analysis of the solution under various conditions of threats is carried out. The influence of negative factors on the construction project during its long-term implementation is considered separately. The analysis of the influence of temporal and probabilistic parameters of the task on the degree of risks in the implementation of construction projects was carried out. Results. The relevance of developing a risk assessment model for the implementation of construction projects is shown, goals and objectives for scientific research are set. The ways of solving the set tasks are given and substantiated. A mathematical model has been developed that makes it possible to estimate the probabilities of finding a construction project in various states, differing in different degrees of risk during the implementation of the project. On the basis of numerical methods, the practical implementation of the model is given for various parameters characteri¬zing the influence of negative factors on the progress of the construction project. The results of the practical implementation of the model are analyzed, recommendations are given for using the model in practice. Conclusion. The presented dynamic risk assessment model for the implementation of construction projects can serve as the basis for building an optimal control system for the progress of construction work and making decisions on the organization of construction activities.

Variational problem of adaptive optimal control. Theoretical and applied computer analysis

The problem of adaptive optimal control of a dynamical system, which belongs to the class of conditional variational problems with moving boundaries, is considered. A variational and computer study of the controlled adaptive motion of a material point is carried out for the problem of the energy quality functional minimizing with a moving, not predetermined right transboundary and in the case when the mass of the point changes depending on the unfixed final time. The problem is solved using the schemes and procedures of the classical calculus of variations, as well as adaptive estimation techniques, including the derivation of the variation of the auxiliary quality functional, the corresponding Euler equations, and the adaptive estimation algorithm. When solving a general conditional variational problem, the obtained closed system of differential equations was studied for the formation of an adaptive optimal control system for a dynamic plant with a given performance functional. The results of the unconditional formulation of the problem are generalized to the case of additional differential (nonholonomic) and holonomic constraints. In a variational adaptive optimal control problem, the transversality condition is formulated in terms of the local programming condition. The developed variational scheme of adaptive optimal synthesis can be used in the calculation and design of controlled dynamic systems. This optimization scheme is also promising for use in systems where operating time is non-fixed in advance. The results achieved in this paper concern obtaining specific equations, expressions, and formulas relative to the model example under study and finding graphs of the main time functions that determine the nature of the movement of the control object and the quality of the corresponding transients. The proposed adaptive optimal control algorithms for purposeful movement of the studied material point were tested in digital mode and showed their effectiveness which makes them promising for further use in more complex nonlinear adaptive systems of dynamic optimal control.

Selection of Weight Coefficients of Quadratic Quality Functional in Solving ADOC Problem in the Letov—Kalman Formulation

For linear stationary one-dimensional control objects, the inverse problem of analytical design of optimal controller (ADOC) is considered, which consists in determining the weight coefficients of the quadratic functional of the optimality of the control process, providing a closed control system with the set values of primary quality indicators (static error, transient time and overshoot). It is analyzed in relation to both the ADOC problem in the Letov-Kalman formulation. A method of its solution is proposed based on the transformation of the ADOR problem to a canonical form in which the control object is described by a matrix differential equation in the Frobenius form, and the quality functional is defined as an integral of the sum of the products of the canonical phase coordinates of the object with the corresponding weight coefficients, as well as the square of the control signal. It is shown that the solution of the inverse canonical ADOC Letov-Kalman problem is determined by the values of only three non-zero weighting coefficients of the criterion, and one of them has a single value. The values of the other two coefficients are proposed to be found in the process of modeling the synthesized optimal control system from the conditions of ensuring for it the values of primary quality indicators no more than the specified ones. The results obtained, presented in the form of Theorems 1 and 2, are extended to the synthesis of astatic control systems, in which an additional integrator is connected to the plant output to obtain astaticism. Since such an "extended" control object is described using a state vector that has the first two phase coordinates of the canonical form, the synthesis of the optimal system is carried out without converting the object description to the canonical form of the phase variable and vice versa. The construction of an astatic control system is illustrated by an example.

Performance analysis on parallel operation of multimode droop controller doubly fed induction generator based wind energy conversion system with Other wind unit, solar units, loads and facts device

Due to their numerous advantages, wind turbines with changeable speed power production systems are increasingly being used. This study proposes the architecture and specifications of an induction turbine-generating wind system, as well as a PI controller-based DC voltage link regulator and optimal torque control system. The suggested control technique as stated in this paper allows the system to function in grid-linked mode as well as the islanded mode and also in parallel with other power generation units, loads, FACTS devices, etc. This paper involves the analysis of different test cases in grid-connected mode as well as an islanded mode with a PV generation unit, passive loads, induction motor loads, and other wind energy generation systems. The paper also includes an analysis of the response of the system with the switching on and off of the other units. MATLAB 2013a thereby validates the system findings and analysis.

Control Analysis of Vehicle Steering System based on Closed-Loop Control Algorithm

When a four-wheel vehicle turns and the steering centre of the front and rear wheels is one point, it is regarded as the theoretical optimal steering of the vehicle and the goal of optimal control. Aiming at the commonly used multi-link steering system, the system control was analysed, according to the structural characteristics and angle relationship. Based on the closed-loop control algorithm, the optimal control of the steering system was designed and analysed, according to the steering control quantity obtained by the target path and parameter feedback. At the same time, the state variables and prediction parameters of the system were analysed. Based on the actual vehicle and steering optimal control system, the changes of various parameters of vehicle operation under no-load condition and turning at 30 km/h were analysed and compared with the theoretical optimal value to verify the effectiveness of the control system. The results show that: the state variables of the control system are predicted by discrete analysis and half step integration, and the accuracy is high. In the steady state turning condition, with the lifting of the vehicle, the radius of the steering track gradually increases, and the vehicle shows obvious understeer characteristics. Under the two working conditions, the characteristic curves obtained by the steering control system are highly consistent with the theoretical values, and the peak error of the two is controlled within 5%, indicating the reliability of the optimal control algorithm, which provides a reference for such design optimization.

Stability analysis and optimal control in an epidemic model on directed complex networks with nonlinear incidence

In this paper, stability and optimal control for SIS epidemic systems with birth and death in directed complex networks are investigated. A class of epidemic systems are constructed based on SIS models combining with two kinds of topological characters as in-degree and out-degree in directed networks, in which the nonlinear incidence rate is introduced that relevant to network’s topology containing the psychological effect coefficient. The disease-free and the endemic equilibria are derived and the epidemic threshold for our systems is obtained. Then, the local stability about the disease-free and the endemic equilibria are discussed via the corresponding Jacobian matrices and the characteristic equation. In addition, global asymptotical stability about two kinds of equilibria are also considered based on the Lyapunov function and stable analysis method. From the view of Pontryagin Minimum Principle, the optimal control issue about the system is also considered, and the corresponding optimal control systems and optimal control tactics are obtained. Several numerical examples are provided to demonstrate the effectiveness of our main method. Meanwhile, by means of the Forward–Backward Sweep method, optimal control systems are solved in the aspect of numeric and the control aim under the derived strategies is achieved.

Dynamics modeling and optimal control for multi-information diffusion in Social Internet of Things

As an ingenious convergence between the Internet of Things and social networks, the Social Internet of Things (SIoT) can provide effective and intelligent information services and has become one of the main platforms for people to spread and share information. Nevertheless, SIoT is characterized by high openness and autonomy, multiple kinds of information can spread rapidly, freely and cooperatively in SIoT, which makes it challenging to accurately reveal the characteristics of the information diffusion process and effectively control its diffusion. To this end, with the aim of exploring multi-information cooperative diffusion processes in SIoT, we first develop a dynamics model for multi-information cooperative diffusion based on the system dynamics theory in this paper. Subsequently, the characteristics and laws of the dynamical evolution process of multi-information cooperative diffusion are theoretically investigated, and the diffusion trend is predicted. On this basis, to further control the multi-information cooperative diffusion process efficiently, we propose two control strategies for information diffusion with control objectives, develop an optimal control system for the multi-information cooperative diffusion process, and propose the corresponding optimal control method. The optimal solution distribution of the control strategy satisfying the control system constraints and the control budget constraints is solved using the optimal control theory. Finally, extensive simulation experiments based on real dataset from Twitter validate the correctness and effectiveness of the proposed model, strategy and method.

Cybernetic model of rational world order under the paradigm of directed evolution

With the rapid advancement in our civilizationʼs technology, the dynamics of a variety of global processes are on the rise as well, the environmental degradation rate increases, competition for access to resources grows, new large-scale epidemics emerge, etc. All of these processes and phenomena have a negative impact on global security and are being studied by scientists to develop recommendations for a world order that will meet the needs of humanity, regardless of race, nationality, socio-cultural and religious affiliation, and will allow for the restoration of the environment. The new principles of the world order should be rooted in the main principle of human security — «the possibility of rational development of civilization». This can be achieved by implementing an optimal control system for the world order. Human security should be considered, in addition to the factors of the direct threat of military conflicts, in the context of climate change and natural disasters, cultural and social development, migration and health care. Considering that the problem of human security and development is an interdisciplinary one, the only way to solve it is to combine the efforts of scientists who specialize in different sciences and to use a transdisciplinary approach that appeals to the creation of a scientific picture of the world based on the systematic integration of scientific knowledge and the Noosphere Theory of Academician Vernadsky V.I.

An industrial virus propagation model based on SCADA system

Supervisory control and data acquisition (SCADA) systems are widely used in the national infrastructure. As more and more SCADA systems have been connected to the Internet, SCADA systems are facing great network security threats, especially attacks from industrial viruses. This paper aims to propose a novel mathematical model of industrial viruses propagation over SCADA systems. Then, the existence and stability of the equilibrium point of this model are studied. To better control the spread of this virus with limited resources, an optimal control system is established for the model. Then, the existence of optimal control is proved, and the corresponding optimal control system is derived. Numerical simulation results show that our proposed control method can effectively control the spread of industrial viruses.

Adaptive stochastic and hybrid nonlinear optimization algorithms for improving the effectiveness of the biological processes at WWTP

Wastewater treatment plays an important factor in the modern world. Insufficient treatment may result in environmental pollution which can further lead to disasters and diseases. However, processes that take place inside wastewater treatment plants (WWTP) are highly complex in nature, therefore it is difficult to design an efficient, optimal control system. The problem regarding biochemical reactions inside Sequential Batch Reactor (SBR) is analyzed in this paper and the optimization problem is defined. Next, chosen optimization methods including both deterministic and metaheuristic algorithms are carefully described. Series of simulation experiments are conducted based on a verified model of SBR from Swarzewo Wastewater Treatment Plant (WWTP) - Northern Poland. The proposed optimal control system allowed to increase the efficiency, improve the quality of outflow (reduction of Chemical Oxygen Demand (COD), total nitrogen (Ntot) and total phosphorus (Ptot)) and reduce wastewater treatment costs.

An OCF-IoTivity enabled smart-home optimal indoor environment control system for energy and comfort optimization

The growing energy demand with diminishing energy resources calls for development of optimal indoor control system through accurate energy and occupant comfort modeling in a smart-home. While some major obstacles faced by smart-home IoT network are heterogeneity and disparate IP frameworks resulting in a connectivity and interoperability issues. In this paper we developed a new Open Connectivity Foundation (OCF) based prediction assisted optimal control framework for optimizing energy consumption and maximizing occupant comfort in smart-home. To the best of our knowledge, we are the first to design a scalable, secure, and inter-operable optimal control solution for smart-home IoT networks. The developed framework offloads machine learning models on IoT device for accurate energy and thermal comfort modeling to enable prediction assisted optimization. The system enables edge analytics using deep learning based inference models for proactive response. For optimization standard Firefly algorithm is modified based on inertia weight approach to achieve improved performance. OCF based optimal actuator control test-bed deployment and real-time experimentation is conducted to evaluate the performance of the system. Empirical investigation verified the effectiveness of proposed framework with energy saving scope of 36.82%, 5 s average response time and 3.36 MS Round Trip Time.

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation.

Machine-Synthesized Control of Nonlinear Dynamic Object Based on Optimal Positioning of Equilibrium Points

When solving an optimal control problem with both direct and indirect approaches, the main technique is to transfer the optimal control problem from the class of infinite-dimensional optimization to a finite-dimensional one. However, with all these approaches, the result is an open-loop program control that is sensitive to uncertainties, and for the implementation of which in a real object it is necessary to build a stabilization system. The introduction of the stabilization system changes the dynamics of the object, which means that the optimal control and the optimal trajectory should be calculated for the object already taking into account the stabilization system. As a result, it turns out that the initial optimal control problem is complex, and often the possibility of solving it is extremely dependent on the type of object and functionality, and if the object becomes more complex due to the introduction of a stabilization system, the complexity of the problem increases significantly and the application of classical approaches to solving the optimal control problem turns out to be time-consuming or impossible. In this paper, a synthesized optimal control method is proposed that implements the designated logic for developing optimal control systems, overcoming the computational complexity of the problem posed through the use of modern machine learning methods based on symbolic regression and evolutionary optimization algorithms. According to the approach, the object stabilization system is first built relative to some point, and then the position of this equilibrium point becomes a control parameter. Thus, it is possible to translate the infinite-dimensional optimization problem into a finite-dimensional optimization problem, namely, the optimal location of equilibrium points. The effectiveness of the approach is demonstrated by solving the problem of optimal control of a mobile robot.

ESTIMATING THE QUALITY FUNCTIONAL IN OPTIMAL CONTROL VARIATIONAL CALCULUS TASKS UNDER THE CHANGES OF THE LEFT-HAND ARGUMENT OF BOUNDARY CONDITION

Estimating the quality functional in optimal control variational calculus tasks under the changes of boundary condition is considered. In control systems, there is a certain permissible change of the controlled parameter based on which the control system is designed. Unlike ordinary control systems, in optimal control systems, there is another indicator - the quality functional (optimality criteria), which also depends on the controlled parameters. Therefore, the permissible range of changes of controlled parameters in optimal control systems should be determined based on the quality functional value’s tolerances. Therefore, estimating the quality functional under the changes of boundary conditions has theoretical and practical importance. It is particularly important for problems solved by numerical methods because it is quite simple for problems solved analytically. In this article, the estimation methods of the quality functional under the changes of left-hand argument of boundary condition in the form of Taylor series with an accuracy of the second member in optimal control variational calculus tasks solved by the indirect nu-merical method are developed. According to the developed method, both the optimization function and the quality functional are functions of the left-hand argument of boundary condition. In other words, the boundary condition parameter is an argument of the optimi-zation function. The mathematical apparatus for determining the specified series coeffi-cients has been developed. These coefficients depend on the partial derivatives of the op-timization function by boundary parameter. The boundary conditions for partial deriva-tive functions of the optimal function by boundary parameters, and the determination methods for these functions using the known optimal function are studied. The truth of the Taylor series coefficients, and the algorithm for their determination are shown experimen-tally.

Design of an Optimal Scheduling Control System for Smart Manufacturing Processes in Tobacco Industry

The whole process of tobacco production is composed of many components, in which their operation and administration are currently independent. It is required to deploy smart manufacturing workflow for the whole production process, in order to realize centralized effective global scheduling. This requires an advanced administration control platform that has strong abilities of multisource data integration and automatic decision support. To bridge such research gap, this paper designs an optimal scheduling control system for smart manufacturing processes of tobacco industry. First of all, this work discusses major characteristics of future-generation production control patterns in intelligent tobacco factories (ITF). Then, a five-layer architecture for optimal scheduling control of ITF is proposed, which contains Internet-of-Things layer, centralized control layer, model layer, platform layer and operation layer. In addition, a production scheduling optimization strategy is also developed for the proposed system to serve as the software algorithm that drives the running of whole smart manufacturing processes. Finally, this paper presents a comparative analysis of the proposed system’s transformation in a cigarette factory. Naturally, the effectiveness of the proposed production optimization scheduling strategy is verified through simulation.