Application Of Control Theory Research Articles

Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: Theory and experimental validation

Abstract This paper adopts a fixed-time method to study the trajectory tracking issue of a quadrotor unmanned aerial vehicle (UAV) under time-varying wind disturbances. Firstly, in order to address the impact of time-varying wind disturbances on UAV, a fixed-time disturbance observer (FxTDO) is constructed to accurately estimate wind disturbances. Secondly, to improve control accuracy and convergence rate, the robust fixed-time controller is designed for the position and attitude system by combining the sliding mode control theory with fixed-time technique. Furthermore, it is rigorously analyzed that the tracking error of the observer and controller can converge to zero via Lyapunov criterion, and the convergence time is independent of the initial state.Finally, the effectiveness and robustness of the designed control strategy are verified by numerical simulations and actual flight experiments, providing an effective connection between control theory and practical applications.

Correction: Chaotic dynamics and zero distribution: implications and applications in control theory for Yitang Zhang’s Landau Siegel zero theorem

Correction: Chaotic dynamics and zero distribution: implications and applications in control theory for Yitang Zhang’s Landau Siegel zero theorem

Symmetry and symmetric transformations in mathematical imaging

The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.

Robust fuzzy-logic flight control for unmanned aerial vehicles (UAVs)

Researches on Unmanned Aerial Vehicles (UAVs) have been recently attracting considerable interest in the field of control theory applications. They are used in a wide range of areas thanks to having the potential of high manoeuvrability, hovering and flying, taking off and landing capabilities. However, to maintain robust control action towards changing conditions of the system is not an easy matter since quadrotor UAVs are highly unstable systems with high precision. Therefore, the main purpose of this study is to control a quadrotor UAV by using a proposed multi-input single-output (MISO) fuzzy-logic controller that ensures robustness if model parameters and trajectory change. For that reason, a 2-dimensional 3 degree-of-freedom quadrotor was used in this study to better evaluate the performance of proposed controller on UAVs. Afterwards, numerical analysis was performed and the findings were analysed. Consequently, the single most striking observation to emerge from the study is that the satisfactory results have been obtained demonstrating that the proposed fuzzy logic controller has remarkable advantage on the robustness of quadrotor UAVs.

Chaotic dynamics and zero distribution: implications and applications in control theory for Yitang Zhang’s Landau Siegel zero theorem

Chaotic dynamics and zero distribution: implications and applications in control theory for Yitang Zhang’s Landau Siegel zero theorem

Dual Quaternion Matrix Equation AXB = C with Applications

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

Planar Walking of a Five-Link Biped Robot over a Stepped Surface with Obstacles of Different Heights and Lengths

A problem of modeling biped locomotion is an actual and complex problem of modern control theory. In the present paper, we deal with a special case when a five-link biped robot with knees moves along a given stepped surface. We describe the robot motion by a hybrid system which consists of a system of ordinary differential equations at the single support phase and an algebraic relation at the double support phase. The main contribution of this paper is the construction of a periodic motion that satisfies a set of conditions inherent in human walking. The results of the paper will be useful to those who are interested in control theory applications.

Maximum Power Point Tracking Control of Offshore Hydraulic Wind Turbine Based on Radial Basis Function Neural Network

A maximum power point tracking control strategy for an affine nonlinear constant displacement pump-variable hydraulic motor actuation system with parameter uncertainty, used within an offshore hydraulic wind turbine, is studied in this paper. First, we used the feedback linearization method to solve the affine nonlinear problem in the system. However, offshore hydraulic wind turbines have strong parameter uncertainty characteristics. This conflict was resolved through the further application of RBF neural network adaptive control theory. So, we combined feedback linearization with RBF adaptive control as the control theory, and then two control laws were compared by setting the pump rate and rating as outputs, respectively. It is shown by the MATLABR2016a/Simulink emulation results that power control is smoother than speed and friendlier for electric networks. It is also shown by the emulation results, in terms of the undulatory wind speed condition, that the feedback linearization–RBF neural network adaptive control strategy has perfect robustness. According to the simulation results, the feedback linearization–RBF neural network adaptive control strategy adopts the RBF neural network to approach complex nonlinear models and solve the parameter uncertainty problem. This control law also avoids the use of feedback linearization control alone, which can result in the system becoming out of control.

Automatic Control and System Theory and Advanced Applications—Volume 2

The aim of the Special Issue on Automatic Control and System Theory and Advanced Applications, the second volume of a previous paper selection, is to emphasize the role of new inventions in the area of automatic control applications [...]

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Optimal Controllers for the Operation of Activated Sludge Treatment Systems

Objective: Application of Optimal Control Theory to the activated sludge process in order to regulate the removal of the carbonaceous part of the organic matter.   Theoretical benchmark: Dynamic models of activated sludge processes are capable of enabling the development of innovative control systems. The Optimal Control Theory, aimed at optimizing the performance of dynamic systems, allows the establishment of control systems that enhance efficiency in adapting to changes in operating conditions, ensuring satisfactory process performance.   Method: The proposed control systems were established from the application of Optimal Control Theory, considering the use of the dynamic model of the activated sludge process presented by International Association on Water Pollution Research and Control. Computer simulations were used to assess the performance of the control systems proposed.   Results and conclusion: The proposed control systems were capable of curbing substantially the oscillations in the concentrations of biomass, of particulate matter produced by the degradation of biomass and those of the inert particulate substrate. The reductions in the oscillations of the slowly biodegradable part of the influent were relatively smaller. The controller was quite effective in leading the wastewater treatment system sooner to the new equilibrium conditions after the imposition of the disturbances in raw effluent.   Implications of research: Development of control systems for activated sludge processes to regulate the removal of the carbonaceous fraction from organic matter.   Originality/value: The establishment of optimal control systems for activated sludge processes can enable greater efficiency and operational capacity, especially in industrial facilities or densely populated urban settlements, where such wastewater treatment systems are most commonly used.

Analysis And Optimization of Automotive Systems Based on PID Control

The development of modern technology has made automation an important part of life. Proportion Integral Derivative (PID) control is a basic control theory of automation which has many applications because of its simple construction and great performance. This article introduces the application of PID control technology in the automotive field. This paper mainly introduces the following aspects: the basic principles and theories of PID control, the challenges of automotive systems and their control, some solutions for PID control in automotive systems, and the improvement and optimization of control. The limitation of the application of traditional control theory in new automotive control have led to the emergence of more optimization algorithms, which can improve the system in more ways. In the future, automotive control systems will continue to be based on PID control as the framework and combined with some optimized new algorithms for practical application. Therefore, understanding PID control is of great significance to clarify the future development of automotive control technology.

A Review on Intelligent Control Theory and Applications in Process Optimization and Smart Manufacturing

In the evolving landscape of manufacturing, the integration of intelligent control theory stands as a pivotal advancement, driving both process optimization and the paradigm of smart manufacturing. This review delves into the multifaceted applications of intelligent control theory, emphasizing its role in equipment, operations, and controls optimization. With a focus on three primary methodologies—fuzzy logic, neural networks, and genetic algorithms—the paper elucidates their biological parallels and their significance in simulation, modeling, and optimization. The transformative potential of smart manufacturing, synonymous with Industry 4.0, is also explored, highlighting its foundation in data, automation, and artificial intelligence. Drawing from a comprehensive analysis of recent literature, the review underscores the growing interest in this domain, as evidenced by the surge in publications and citations over the past decade. The overarching aim is to provide contemporary discourse on the applications and implications of intelligent control theory in the realms of process optimization and smart manufacturing.

Feedback delay of sports intelligent learning system based on model predictive control and artificial intelligence

At present, in terms of model predictive control theory and model applications, two-layer segmented linear grid models are dominant. The two-layer piecewise linear lattice model is more effective, does not require too many parameters and is easy to calculate. Since the multi-layer model predictive control is based on a two-layer model, it is very important to study the mechanism and optimization methods of the two-layer model. Artificial intelligence comes from computer science. It tries to understand the nature of intelligence and create new intelligent machines that can react like human intelligence. Research in this field involves robotics, speech recognition, image recognition, natural language processing, etc. Since the emergence of artificial intelligence, theory and technology have gradually matured, and its application fields have also increased. The technological products created by artificial intelligence will embody the development of human wisdom in the future. Sports intelligence learning was first proposed by Lins. Linsley found that under laboratory conditions, by observing and recording the learner's behavior frequency and reaction speed, and adjusting the learning activities based on this, a better learning effect can be obtained. The combination of sports intelligence learning and behaviorist learning theory forms a systematic and accurate teaching method. Video system feedback delayed learning is a part of multimedia education technology. In recent years, multimedia technology has been widely used in various educational fields. By reviewing the application research of multimedia teaching technology in education, we have determined the areas related to the delay of the video system feedback, and guided the application research of the video feedback system in education.

Identify the effect of government regulations on the live streaming e-commerce

PurposeOn December 20, 2021, Viya, a social media influencer (SMI) with the largest number of followers in China, was exposed for having evaded RMB 643 million in taxes during 2019 and 2020. Consequently, she was fined a total of RMB 1.341 billion by the tax authorities. While the strict government regulations demonstrated in the Viya event may build confidence in the consumers for future purchases, the exposure of issues and problems through implementation of the stronger government regulations may warn consumers off. Thus, the main objective of this paper is to examine the effect of government regulations on consumers' usage intentions of live streaming e-commerce by taking the Viya event as an example.Design/methodology/approachThe authors consider both the positive effect of consumers' perceived benefits of the government regulations and the negative effect of their perceived risks of the Viya event on the usage intentions of live streaming e-commerce. After collecting 314 subjects with diverse gender, ages, education levels and income profiles, the data are processed by partial least squares-based structural equation modeling (PLS-SEM) and SmartPLS software.FindingsThe results demonstrate that strict government regulations can build trust in consumers of live streaming e-commerce by increasing the perceived benefits of restricting the behavior of SMIs. Among the potential perceived risks (social risk, safety risk and psychological risk), the safety risk is supported to have a negative effect on consumers' trust in live streaming e-commerce platforms. Besides, the authors have also identified different types of usage intentions in live streaming e-commerce, i.e. watching intention and purchase intention, and have empirical support for the positive relationships between the consumers' trust in live streaming e-commerce platforms and different usage intentions.Originality/valueThe authors' findings contribute to the application of commitment-trust theory, institutional theory and organizational control theory in the context of the live streaming e-commerce industry. Particularly, the authors use the Viya event as an example to quantitatively examine the effects of strict government regulations, which enriches the existing literature on this topic.

Margins of postural stability in Parkinson's disease: an application of control theory.

Introduction: Postural instability is a restrictive feature in Parkinson's disease (PD), usually assessed by clinical or laboratory tests. However, the exact quantification of postural stability, using stability theorems that take into account human dynamics, is still lacking. We investigated the feasibility of control theory and the Nyquist stability criterion-gain margin (GM) and phase margin (PM)-in discriminating postural instability in PD, as well as the effects of a balance-training program. Methods: Center-of-pressure (COP) data of 40 PD patients before and after a 4-week balance-training program, and 20 healthy control subjects (HCs) (Study1) as well as COP data of 20 other PD patients at four time points during a 6-week balance-training program (Study2), collected in two earlier studies, were used. COP was recorded in four tasks, two on a rigid surface and two on foam, both with eyes open and eyes closed. A postural control model (an inverted pendulum with a Proportional-integral-derivative (PID) controller and time delay) was fitted to the COP data to subject-specifically identify the model parameters thereby calculating |GM| and PM for each subject in each task. Results: PD patients had a smaller margin of stability (|GM| and PM) compared with HCs. Particularly, patients, unlike HCs, showed a drastic drop in PM on foam. Clinical outcomes and margins of stability improved in patients after balance training. |GM| improved early in week 4, followed by a plateau during the rest of the training. In contrast, PM improved late (week 6) in a relatively continuous-progression form. Conclusion: Using fundamental stability theorems is a promising technique for the standardized quantification of postural stability in various tasks.

An optimal control model for Covid-19 spread with impacts of vaccination and facemask

A non-linear system of differential equations was used to explain the spread of the COVID-19 virus and a SEIQR model was developed and tested to provide insights into the spread of the pandemic. This article, which is related to the aforementioned work as well as other work covering variations of SIR models, Hermite Wavelets Transform, and also the Generalized Compartmental COVID-19 model, we develop a mathematical control model and apply it to represent optimal vaccination strategy against COVID-19 using Pontryagin's Maximum Principle and also factoring in the effect of facemasks on the spread of the virus. As background work, we analyze the mathematical epidemiology model with the facemask effect on both reproduction number and stability, we also analyze the difference between confirmed COVID-19 cases of the Quarantine class and anonymous cases of the Infectious class that is expected to recover. We also apply control theory to mine insights for effective virus spread prevention strategies. Our models are validated using Matlab mathematical model validation tools. Statistical tests against data from Jordan are used to validate our work including the modeling of the relation between the facemask effect and COVID-19 spread. Furthermore, the relation between control measure ξ, cost, and Infected cases is also studied.

Contribution of peri-urban land use and agriculture to entropy and food of mega-cities: On sustainability, planning by control theory and recycling of organics.

In this article we propose an ecological economics orientation of peri-urban development, looking at land use planning, local food and entropy. Based on a mathematical model, we present an operational concept of minimizing negative externalities within a given population. The model applies control theory. The concept is introduced to facilitate closing cycles, conduct spatial planning and reduce costs to achieve the ecological target of improved entropy. To this end, we look at more soundly defined metropolitan areas. An emphasis is placed on optimally assuring space for urban agriculture and on enabling recycling in ever-growing cities. Our concept is grounded in the use of peri-urban agriculture and regional food provision as an integrated system, which is based on the recycling of organic matter. Firstly, we reference current unhealthy developFfigments and show how cycles were removed as growth occurred. Secondly, as market-oriented city expansions showed limited scope for peri-urban farming, we suggest entering into regional planning. Planning shall ensure a better use of space and can be based on organic matter recycling (composting, slurry, etc.). The article provides a theoretical background for the occurrence of modified land use (systems). These systems shall alleviate some external burdens of large and growing cities. The approach looks at ecological, economic and social aspects in parallel, to outline principles for more sustainable land use, including peri-urban land. Methodologically we offer land use modelling, looking at interactions of industry, residence, and farming. The functions of a city are integrated into a methodical approach of distance from centre to periphery.

Synthesize the optimal control law for the antenna transmission system of the missile seeker

The appearance in the armed forces of some countries super-maneuverable aircraft has posed the problem of synthesizing the angle measuring equipment of the missile seeker with higher requirements for accuracy, fast acting, and stability when tracking the target. However, the operating principle of current angle measuring equipment does not allow simultaneous improvement of all the necessary criteria, even though such principles are based on the generation of the evaluation signals of angular coordinates and angular speed of line of sight in a loop circuit. Based on the application of optimal control theory, it is possible to synthesize the system’s many loop circuits, which simultaneously achieve the best criteria in terms of accuracy, impact speed, as well as tracking stability, and consumption energy for the control process.

Controlling a Pandemic: An Account of Successfully Applying Control Theory to the Covid-19 Pandemic in Denmark [Applications of Control]

Controlling a Pandemic: An Account of Successfully Applying Control Theory to the Covid-19 Pandemic in Denmark [Applications of Control]