Control Theory Research Articles

Unscented Trajectory Optimization

In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was introduced by the authors about a decade ago, it is reintroduced in this paper as a special instantiation of tychastic optimal control theory. Tychastic optimal control theory (from Tyche, the Greek goddess of chance) avoids the use of a Brownian motion and the resulting Itô calculus even though it uses random variables across the entire spectrum of a problem formulation. This approach circumvents the enormous technical and numerical challenges associated with stochastic trajectory optimization. Furthermore, it is shown how a tychastic optimal control problem that involves nonlinear transformations of the expectation operator can be quickly instantiated using the unscented transform. These nonlinear transformations are particularly useful in managing trajectory dispersions, be they associated with path constraints or targeted values of final-time conditions. This paper also presents a systematic and rapid process for formulating and computing the most desirable tychastic trajectory using the unscented transform. Numerical examples are used to illustrate how unscented trajectory optimization may be used for risk reduction and mission recovery caused by uncertainties and failures.

Minimizing the penalized goal-reaching probability with multiple dependent risks

We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.

Managers’ Toxic Masculinity Erodes Employees’ Work Ethics in Private Institutions of DRC’s City of Bukavu

Purpose: This research has explored views of employees in Bukavu (DRC) private institutions regarding ways managers’ toxic masculinity damages employers’ work ethics at workplace. Methodology: Researchers conducted this qualitative study in the city of Bukavu between April and June 2024 with randomly selected 25 respondents from five private institutions. Respondents were Congolese females and males whose ages varied between 19 and 63. Data was collected via face-to-face focus group discussions, with in-depth interviews. The theories of masculinity and control guided the research. Masculinity posits that managers must exert power and control over their employees at workplace. Managers resorting to toxic masculinity damage the ethics of their workers, which can affect productivity. Findings: Results reveal how a manager may use toxic masculinity to deride the workers, which kills their appreciation and motivation for work. Managers applying domination, homophobia, giving poor and unfair salaries, abusing employees and discriminating against them are perpetuating toxic masculinity in their institutions. These factors are demotivating and destructive agents for employees’ ethics at work because they convey toxic masculinity through power and control, all causing work unproductivity. Unique Contribution to Theory, Practice and Policy: The research suggests that employers should develop progressive masculinity at work by valuing and respecting the workers. The perspective can boost collaboration; sustain commitment and harmony at work. Socializing constructive manliness can create a conducive work environment in private institutions of Bukavu, increase workers’ commitment to work, as well as the production.

Analysis of User Interfaces for Ground Control Stations of Unmanned Aerial Vehicles

Introduction. In the modern world, software (SW) is updated daily, particularly for ground control stations (GCS) of unmanned aerial vehicles (UAVs). These systems ' user interfaces (UI) ensure operator interaction with the drone, flight control, mission planning, and realtime data acquisition. These interfaces must be functional, convenient, and intuitive, allowing operators to perform their tasks effectively. Examining global experience allows for an evaluation of existing systems and the identification of areas for improvement. Important aspects include creating intuitive UIs to prevent information overload, ensuring situational awareness, adapting to extreme conditions, and integrating with other systems. The use of virtual and augmented reality technologies, as well as artificial intelligence, can enhance the functionality and convenience of GCS. Such analysis will help in creating safe, efficient, and reliable systems for UAV control. The purpose of the paper is to investigate and conduct a comprehensive analysis of existing user interfaces of software for UAV ground control stations, focusing on their functional capabilities and ease of use. Methods. The following methodological tools were used: concepts of intellectualization of information technologies, the theory of intelligent control, the methodology of building autonomous systems, decision-making theory, and artificial intelligence theory. Results. A review of global experience in user interface development was conducted. The UIs of each of the studied software were analyzed, and their functional capabilities were assessed, identifying their strengths and weaknesses. Comparative tables of interface products were compiled based on their functional capabilities and UI usability levels. Generalized recommendations were prepared for creating a unified interface that combines the best features of existing solutions and addresses their shortcomings. Conclusions. The analysis of GCS UI design for UAVs showed that all systems have strengths and weaknesses. The UI of the Mission Planner software has the most extensive capabilities, but it also requires improvement. Future development should add roles for military pilots and operators, develop a more intuitive and user-friendly interface that meets user needs, and simplify SW settings. For working in extreme conditions, the interface needs to be optimized. Enhancements in data visualization will help make information clear and easy to understand, which is critically important in fast-paced and dangerous situations. Keywords: user interface, ground control station, UAV, virtual reality, augmented reality.

ПРОБЛЕМЫ РЕАЛИЗАЦИИ СИСТЕМ ПОЛУАВТОМАТИЧЕСКОГО УПРАВЛЕНИЯ, ВКЛЮЧАЮЩИХ КОНТУР ОБРАТНОЙ СВЯЗИ ПО УСИЛИЮ

The issues of force-torque sensing in semi-automatic systems are considered. The paper describes the main control principles in ergatic systems from the viewpoint of automatic control theory, considers a method for improving the control quality by introducing additional feedback for the operator. The work proposes force-torque sensing as the most promising feedback channel for the implementation, describes the relevance of this channel in the fulfilled automatic control systems, gives examples. A description of the feedback loop for the efforts on the manipulator’s working element is given. The work highlights the following as the main problems in implementing the considered semi-automatic systems: the kinematic chain influence, filtering and delay, gravity compensation, as well as the problem of the natural feedback loop.

К совершенствованию технологии планирования транспортных процессов взаимодействия железнодорожных линий различных категорий

Purpose: increasing the efficiency of the transport network based on the developed balanced system of indicators for the interaction of railway lines of various categories. Methods: methods of control theory, system analysis, synthesis and mathematical modeling, theory of transport processes and systems, and transport planning methods are used. Results: a set of indicators that influence the interaction of railway lines of various categories is substantiated, based on a balanced system of indicators, which makes it possible to develop corrective measures to optimize the transportation process. Practical significance the implementation of the proposed solutions allows us to develop and specify a program to increase the efficiency of operation of low-intensity public railway lines and adjust scheduled transportation on these lines.

On separability of semigroups: application to models of physics and discrete optimization

Nilpotent semigroups are used in various fields of physics to model processes like system decay in quantum mechanics, state transitions in statistical mechanics, and simplifying dynamical systems. They also assist in optimizing control processes. The set of nilpotent matrices forms a semigroup and plays a key role in Jordan decomposition, which has many physical applications. In quantum mechanics, the Jordan form helps analyze linear operators on Hilbert spaces, especially with systems involving eigenvalue multiplicities. In vibration analysis, it aids in studying normal modes of mechanical systems with degenerate frequencies. Additionally, Jordan decomposition simplifies control theory for linear time-invariant systems, stability analysis in dynamical systems, and the behavior of coupled oscillators, as well as solving systems of linear differential equations. Certainly, the semigroup theory has even more applications in theoretical computer science: suffice it to say, for example, that some authors identify semigroups and finite automata. In this paper, we address the problem of P-separability of semigroups with respect to three key predicates: equality-separability, divisibility-separability, and subsemigroup-separability, achieved through homomorphisms into a nilpotent semigroup. We present some significant results that advance the understanding of these concepts.

A Data-Driven Predictive Control Method for Modeling Doubly-Fed Variable-Speed Pumped Storage Units

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources.

Microstate D as a Biomarker in Schizophrenia: Insights from Brain State Transitions.

Objectives. There is a significant correlation between EEG microstate and the neurophysiological basis of mental illness, brain state, and cognitive function. Given that the unclear relationship between network dynamics and different microstates, this paper utilized microstate, brain network, and control theories to understand the microstate characteristics of short-term memory task, aiming to mechanistically explain the most influential microstates and brain regions driving the abnormal changes in brain state transitions in patients with schizophrenia. Methods. We identified each microstate and analyzed the microstate abnormalities in schizophrenia patients during short-term memory tasks. Subsequently, the network dynamics underlying the primary microstates were studied to reveal the relationships between network dynamics and microstates. Finally, using control theory, we confirmed that the abnormal changes in brain state transitions in schizophrenia patients are driven by specific microstates and brain regions. Results. The frontal-occipital lobes activity of microstate D decreased significantly, but the left frontal lobe of microstate B increased significantly in schizophrenia, when the brain was moving toward the easy-to-reach states. However, the frontal-occipital lobes activity of microstate D decreased significantly in schizophrenia, when the brain was moving toward the hard-to-reach states. Microstate D showed that the right-frontal activity had a higher priority than the left-frontal, but microstate B showed that the left-frontal priority decreased significantly in schizophrenia, when changes occur in the synchronization state of the brain. Conclusions. In conclusion, microstate D may be a biomarker candidate of brain abnormal activity during the states transitions in schizophrenia, and microstate B may represent a compensatory mechanism that maintains brain function and exchanges information with other brain regions. Microstate and brain network provide complementary perspectives on the neurodynamics, offering potential insights into brain function in health and disease.

The Influence of Temperament, Theory of Mind, Inhibitory Control, and Prosocial Behavior on Child Anxiety Symptoms in the First Five Years of Life.

Anxiety disorders are among the most prevalent of all mental health disorders, often originating in early childhood and extending into later childhood, adolescence, and adulthood. Determining salient risk factors that precede their development is important for prevention and intervention efforts. Towards this end, we examined the role of temperament, theory of mind, inhibitory control, and prosocial behavior on child anxiety symptoms in the first 5years of life. A community sample of children and their parents (N = 399) enrolled in a longitudinal study of emotion processing were assessed when the children were infants and at ages 2years, 3years, and 5years. Linear mixed models and linear regression models revealed that greater anxiety at 5years was associated with greater negative affectivity and behavioral inhibition, lower effortful control, lower theory of mind scores on the "desires" domain, and higher scores on the "intentions" domain (assessed from infancy to 3years of age). These characteristics may be useful to assess in clinical settings to evaluate a patient's risk for developing anxiety. They may also be useful in developinginterventions targeting specific vulnerabilities.

The Overstated Challenge: Analysing the Challenge of Southern Criminology to the Hegemony of Northern Criminology and its Implications for Criminological Theory in the 21st Century

In an era marked by the escalating globalisation of crime, the import of Southern criminology has progressively transitioned from a marginalised field to a central focus in research.[1] This transition presents theoretical challenges to criminology in the Northern Hemisphere.[2] This essay posits that while Southern criminology challenges Northern criminology’s hegemony, these challenges are ultimately overstated. Recognising and addressing these challenges is imperative for improving the epistemological framework and theoretical contributions of criminology, thereby equipping it to confront 21st-century criminal phenomena more effectively. [1] Matthews, Roger. “False Starts, Wrong Turns and Dead Ends: Reflections on Recent Developments in Criminology.” Critical Criminology 25, no. 4 (2017): 577-591. [2] Greenberg, David F. “The Weak Strength of Social Control Theory.” Crime & Delinquency 45, no. 1 (1999): 66–81.

Behavioral swarms: A mathematical theory toward swarm intelligence

This paper presents a mathematical theory of behavioral swarms, where the state of interacting entities, which are called active particles, includes in addition to position and velocity, an internal variable, called activity, which has the ability to interact with mechanical variables thus affecting the interaction rules. In turn, the mechanical variables can modify the dynamics of activity variable. This approach is useful for describing the dynamics of living systems with a finite number of interacting entities. This paper provides a general conceptual framework that extends the pioneering work [N. Bellomo, S.-Y. Ha and N. Outada, Towards a mathematical theory of behavioral swarms, ESAIM: Control Theory Var. Calculus 26 (2020) 125, https://doi.org/10.1051/cocv/2020071 ]. The theory is firstly developed for the constant number of active particles. Then, it is considered for the case of particles tending to infinity. This theory is useful for describing the dynamics of living systems. Therefore, it provides the conceptual basis for developing a mathematical theory of behavioral swarms, which naturally lead to the study of a theory of swarm intelligence. A study of the dynamics of swarms shows how the theory can be applied to real world collective dynamics.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies.

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Exploring Factors Related to the Process of Desistance from Crime: A Qualitative Study of Females in the UK

ABSTRACT Less is known about the process of desistance from crime for females within the criminal justice system. The current study explored the views and experiences in a sample of adult female offenders in the UK. Ten women took part in semi-structured interviews. Data were analyzed using thematic analysis. The following themes were identified: Skills and Attributes; Support; Purpose in Life; Risk Factors; and Consequences. The findings provide support for existing theories of desistance including cognitive transformation theory, social control and identity theory of desistance. The findings add to the growing evidence in the field of desistance from crime in female offenders.

Backward Uniqueness for 3D Navier–Stokes Equations With Non-Trivial Final Data and Applications

Abstract Presented is a backward uniqueness result of bounded mild solutions of 3D Navier–Stokes Equations in the whole space with non-trivial final data. A direct consequence is that a solution must be axi-symmetric in $[0, T]$ if it is so at time $T$. The proof is based on a new weighted estimate that enables to treat terms involving Calderon–Zygmund operators. The new weighted estimate is expected to have certain applications in control theory when classical Carleman-type inequality is not applicable.

Characterizing the dynamics, reactivity and controllability of moods in depression with a Kalman filter.

Mood disorders involve a complex interplay between multifaceted internal emotional states, and complex external inputs. Dynamical systems theory suggests that this interplay between aspects of moods and environmental stimuli may hence determine key psychopathological features of mood disorders, including the stability of mood states, the response to external inputs, how controllable mood states are, and what interventions are most likely to be effective. However, a comprehensive computational approach to all these aspects has not yet been undertaken. Here, we argue that the combination of ecological momentary assessments (EMA) with a well-established dynamical systems framework-the humble Kalman filter-enables a comprehensive account of all these aspects. We first introduce the key features of the Kalman filter and optimal control theory and their relationship to aspects of psychopathology. We then examine the psychometric and inferential properties of combining EMA data with Kalman filtering across realistic scenarios. Finally, we apply the Kalman filter to a series of EMA datasets comprising over 700 participants with and without symptoms of depression. The results show a naive Kalman filter approach performs favourably compared to the standard vector autoregressive approach frequently employed, capturing key aspects of the data better. Furthermore, it suggests that the depressed state involves alterations to interactions between moods; alterations to how moods responds to external inputs; and as a result an alteration in how controllable mood states are. We replicate these findings qualitatively across datasets and explore an extension to optimal control theory to guide therapeutic interventions. Mood dynamics are richly and profoundly altered in depressed states. The humble Kalman filter is a well-established, rich framework to characterise mood dynamics. Its application to EMA data is valid; straightforward; and likely to result in substantial novel insights both into mechanisms and treatments.

Identifying limit reference points for robust harvest control rules in fisheries management

Risk and uncertainty are intrinsic characteristics of natural resources that must be taken into account in their management. Harvest control rules (HCR) used to be the central management tool to control stock fisheries in an uncertain context. A typical HCR determines fishing mortality as a linear relationship of the biomass binding only when the biomass is above a critical risk value. Choosing the linear relationship and the risk value is a complex task when there is uncertainty because it requires a high level of data and an in-deep knowledge of the stock. This paper fully characterizes robust HCRs that explicitly include scientific uncertainty using the robust control theory approach. Our theoretical findings show that under uncertainty: i) Constant HCRs are not robust; ii) Robust HCRs show a steeper linear relationship between fishing mortality and biomass and a higher value of biomass to be consider at risk than non-robust HCRs. From the implementation viewpoint, we assume a three-sigma rule and show that robustness is achieved by selecting a fishing mortality such that its deviation from the fishing mortality target is twice the deviation of the biomass from the biomass target, and the critical value of the biomass (the point below which fishing should cease, or become as close to zero as possible) is half of the biomass associated with the maximum sustainable yield when this is the target.

Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach

In engineering and applied sciences, several physical phenomena can be more precisely characterized by employing nonlinear fractional partial differential equations. The primary goal of this research is to examine the traveling wave solution in closed form for the nonlinear acoustic wave propagation model known as the time fractional simplified modified Camassa–Holm equation, which is used to explain the unidirectional propagation of shallow-water waves with non-hydrostatic pressure and explains the dispersion properties of numerous phenomena like fluid flow, control theory, liquid drop patterning in plasma, acoustics, fusion, and fission processes, etc. The utmost potential approach, namely the new auxiliary equation technique, is applied for analyzing the time nonlinear fractional simplified modified Camassa-Holm equation in the logic of the newest established truncated M-fractional derivative. The fractional partial differential equations have been transformed to the ordinary differential equation using the complex wave transformation in the sense of truncated M-fractional derivative. A variety of soliton solutions, including anti-kink, single soliton, anti-bell, bell, kink, multiple soliton, double soliton, singular-kink, compacton shape, periodic shape, and so many, are displayed in the diagram of 3D and contour plots by taking into account a number of various parameters. It is essential to point out that all derived outcomes are directly compared to the original solutions to certify their exactness. Results show that the used scheme is capable, simple, and straightforward and can be useful to a variety of complex phenomena. The acquired results are unique for the model equation and could be applied to the analysis of several nonlinear study fields.

Features of the information and control system of the car's hybrid power plants

Abstract. Problem. Until now, a number of features of IBS power plants of electric and hybrid cars remain unexplored. The applied IIUS analysis and synthesis methods do not pay enough attention to the multi-criteria nature of the arising optimization tasks. Management adaptation methods to changingexternal operating conditions are insufficiently effective. These circumstances do not allow to fully reveal the potential possibilities of IISD power plants of electric and hybrid cars. This determines the relevance of improvement and development of new methods of modeling and optimization of IIUS control of power plants of electric and hybrid cars based on modern theory of automatic control, vector optimization, neural network and neuro-fuzzy adaptive methodology. A methodology for the construction of IIUS invariant to various power plants of electric and hybrid cars has been developed for operational management of modes according to quality, energy and other criteria. Results. The mathematicalsupport of the "Recovery" mode differs from classical problems of optimal control in that it allows changing the parameters of the control power plant, its model type, limit values for control influences, and phase coordinates. Originality. The core of the IICS GSU software is a knowledge base, in which procedural knowledge is presented in the form of frames that implement the algorithmic support of IICS GSU. The knowledge base has a stratified, hierarchical structure that reflects an integrated graph of the synthesis technology of the ZOU solution. The content of the frames of the knowledge base ensures the search for a solution to the ZOU problem in the state space. Frames contain slots that hold not only specific data but also the names of procedures that process them according to a given algorithm. Some frames contain slots filled with product rules. During the creation of the knowledge base of the research prototype, work was carried out on the unification of frame names, which makes it possible to quickly build the knowledge bases of working prototypes. Knowledge frames are a set of classes developed in a visual programming environment. Practical value. The resulting optimal program is worked out using simulation modeling modules, which include direct modeling of systems in multiple states of operation, and if it satisfies the specified requirements, the resulting data is converted into a file containing optimal control influences, which is stored in the database.

Event-triggered adaptive neural inverse optimal output-feedback control of steer-by-wire vehicle systems with prescribed performance

In this article, an event-triggered adaptive neural network (NN) output-feedback inverse optimal control issue is investigated for the steer-by-wire vehicle (SBWV) systems. Firstly, NNs are utilized to approximate the unknown nonlinear dynamics and the auxiliary system of SBWV systems is established. Then, a NN state observer is constructed to estimate the unmeasured states. To obtain better tracking performance, the prescribed performance technique is introduced to constrain the tracking error. An event-triggered mechanism (ETM) is established to decrease the numbers of controller execution times. Subsequently, an event-triggered adaptive NN inverse optimal output-feedback control algorithm is proposed by employing the backstepping control theory. It is proved that the developed control method can not only ensure the stability of the SBWV systems, but also guarantee the tracking error does not exceed the prescribed performance bound and converges to a small neighborhood of zero. Finally, simulation results are given to verify the validity of the proposed control method.