Application Of Control Theory Research Articles

Optimal control of a crop irrigation model under water scarcity

AbstractWe consider a simple crop irrigation model and study the optimal control which consists of maximizing the biomass production at harvesting time. A specificity of this work is to impose a quota on the water used for irrigation, in a context of limited resources. The model is written as a 2d non‐autonomous dynamical system with a state constraint, and a non‐smooth right member given by threshold‐based soil and crop water stress functions. We show that when the water quota is below the threshold giving the largest possible production, the optimal strategy consists of irrigating once. We then show that the optimal solution can have one or several singular arcs, and therefore be better than simple bang‐bang controls, as commonly used. The gains over the best bang‐bang controls are illustrated on numerical simulations. These new feedback controls that we obtain are a promising first step towards the concrete application of control theory to the problem of optimal irrigation scheduling under water scarcity.

Reliability-based stochastic optimal control of frame building under near-fault ground motions

Most of stochastic optimal control methods were developed on the basis of Itô stochastic differential equation, which assumes that the external excitation is white Gaussian noise or filtered white Gaussian noise. However, this assumption is far from the real excitations, which hinders the applications of stochastic optimal control theory. In this paper, the reliability-based stochastic optimal control via direct probability integral method (DPIM) for building structure is proposed, which is applicable to performance-based design of general control systems of linear structures under non-stationary and non-white random excitations. Firstly, the DPIM is utilized to accurately and efficiently compute dynamic reliability of the controlled system. Then, the reliability-based objective function is suggested to optimize the parameters of the placed control devices of building structure, and reliability-based maximum story controllability index is established to determine the optimal placement of control devices, thus fulfilling the stochastic optimal control of structure. Finally, a 10-story shear frame building controlled by active tendons under random excitations of near-fault earthquake ground motions verifies the effectiveness of the proposed optimal control method. Moreover, the optimal control schemes of frame structure under near-fault non-pulse and impulsive ground motions are compared, indicating that the velocity pulses of near-fault ground motions impose significant effect on structural responses, and the more control energy is needed for guaranteeing structural safety.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

A Study on Distributed Optimization over Large-Scale Networked Systems

Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high fault-tolerant and extremely scalable compared with centralized optimization. Centralized solution methods are not suitable for many application domains that consist of large number of networked systems. In general, these large-scale networked systems cooperatively find an optimal solution to a common global objective during the optimization process. Thus, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. This paper presents an analysis that provides an overview of decomposition methods as well as currently existing distributed methods and techniques that are employed in large-scale networked systems. A detailed analysis on gradient like methods, subgradient methods, and methods of multipliers including the alternating direction method of multipliers is presented. These methods are analyzed empirically by using numerical examples. Moreover, an example highlighting the fact that the gradient method fails to solve distributed problems in some circumstances is discussed under numerical results. A numerical implementation is used to demonstrate that the alternating direction method of multipliers can solve this particular problem, by revealing its robustness compared with the gradient method. Finally, we conclude the paper with possible future research directions.

Model properties for efficient synthesis of nonblocking modular supervisors

Supervisory control theory provides means to synthesize supervisors for systems with discrete-event behavior from models of the uncontrolled plant and of the control requirements. The applicability of supervisory control theory often fails due to a lack of scalability of the algorithms. This paper proposes a format for the requirements and a method to ensure that the crucial properties of controllability and nonblockingness directly hold, thus avoiding the most computationally expensive parts of synthesis. The method consists of creating a control problem dependency graph and verifying whether it is acyclic. Vertices of the graph are modular plant components, and edges are derived from the requirements. In case of a cyclic graph, potential blocking issues can be localized, so that the original control problem can be reduced to only synthesizing supervisors for smaller partial control problems. The strength of the method is illustrated on two case studies: a production line and a roadway tunnel.

Nonlinear Control System Design of an Underactuated Robot Based on Operator Theory and Isomorphism Scheme

The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully actuated robot, it has many advantages, such as energy, material, and space saving. Therefore, it has high research value in both control theory and practical applications. Swing-up is a mechanism with two links, which mimics a gymnast performing a horizontal bar movement. Over the past few decades, many sufficiently robust control techniques have been developed for a fully actuated robot but almost none of them can be directly applicable to an underactuated robot system. The reason is that such control techniques require certain assumptions that are valid only for fully actuated robot systems but not for underactuated ones. In this paper, a control system design method for underactuated robots based on operator theory and an isomorphism scheme is first proposed. Bezout identity is designed using isomorphism. The effectiveness of the design method is confirmed by simulation. The simulation results show that the performances, such as robust stability and response time, of an underactuated robot control system are improved.

A distributed-parameter control system using electromagnetic neural stimulation for human–machine perception interface

ABSTRACT This article presents a new design of a distributed-parameter control system for human–machine perception interface, which is capable of precisely stimulating the neural systems with electromagnetic fields. By discretising the neural systems, a state-space representation of the electromagnetic stimulation is developed to facilitate the following design and analysis. A forward controller with multiple inputs and multiple outputs is consequently designed to estimate the excitation current. This novel approach enables the applications of the well-established control theory to analyse the system. The feasibility and accuracy of the control system are numerically illustrated and validated with the applications of Transcranial Magnetic Stimulation (TMS) and retinal stimulation. The results indicate that the newly designed control system can not only generate electromagnetic stimulation with better attenuation and focality than the most widely used Figure-8 coil, but also transmit the patterns extracted from images with electromagnetic stimulations to human retinas.

Control theory helps to resolve the measles paradox.

Measles virus (MV) is a highly contagious respiratory morbillivirus that results in many disabilities and deaths. A crucial challenge in studying MV infection is to understand the so-called ‘measles paradox’—the progression of the infection to severe immunosuppression before clearance of acute viremia, which is also observed in canine distemper virus (CDV) infection. However, a lack of models that match in vivo data has restricted our understanding of this complex and counter-intuitive phenomenon. Recently, progress was made in the development of a model that fits data from acute measles infection in rhesus macaques. This progress motivates our investigations to gain additional insights from this model into the control mechanisms underlying the paradox. In this paper, we investigated analytical conditions determining the control and robustness of viral clearance for MV and CDV, to untangle complex feedback mechanisms underlying the dynamics of acute infections in their natural hosts. We applied control theory to this model to help resolve the measles paradox. We showed that immunosuppression is important to control and clear the virus. We also showed under which conditions T-cell killing becomes the primary mechanism for immunosuppression and viral clearance. Furthermore, we characterized robustness properties of T-cell immunity to explain similarities and differences in the control of MV and CDV. Together, our results are consistent with experimental data, advance understanding of control mechanisms of viral clearance across morbilliviruses, and will help inform the development of effective treatments. Further the analysis methods and results have the potential to advance understanding of immune system responses to a range of viral infections such as COVID-19.

Endurance and avoidance response patterns in pain patients: Application of action control theory in pain research.

BackgroundIdentifying pain-related response patterns and understanding functional mechanisms of symptom formation and recovery are important for improving treatment.ObjectivesWe aimed to replicate pain-related avoidance-endurance response patterns associated with the Fear-Avoidance Model, and its extension, the Avoidance-Endurance Model, and examined their differences in secondary measures of stress, action control (i.e., dispositional action vs. state orientation), coping, and health.MethodsLatent profile analysis (LPA) was conducted on self-report data from 536 patients with chronic non-specific low back pain at the beginning of an inpatient rehabilitation program. Measures of stress (i.e., pain, life stress) and action control were analyzed as covariates regarding their influence on the formation of different pain response profiles. Measures of coping and health were examined as dependent variables.ResultsPartially in line with our assumptions, we found three pain response profiles of distress-avoidance, eustress-endurance, and low-endurance responses that are depending on the level of perceived stress and action control. Distress-avoidance responders emerged as the most burdened, dysfunctional patient group concerning measures of stress, action control, maladaptive coping, and health. Eustress-endurance responders showed one of the highest levels of action versus state orientation, as well as the highest levels of adaptive coping and physical activity. Low-endurance responders reported lower levels of stress as well as equal levels of action versus state orientation, maladaptive coping, and health compared to eustress-endurance responders; however, equally low levels of adaptive coping and physical activity compared to distress-avoidance responders.ConclusionsApart from the partially supported assumptions of the Fear-Avoidance and Avoidance-Endurance Model, perceived stress and dispositional action versus state orientation may play a crucial role in the formation of pain-related avoidance-endurance response patterns that vary in degree of adaptiveness. Results suggest tailoring interventions based on behavioral and functional analysis of pain responses in order to more effectively improve patients quality of life.

Control Theory and Cancer Chemotherapy: How They Interact.

Control theory arises in most modern real-life applications, not least in biological and medical applications. In particular, in biological and medical contexts, the role of control theory began to take shape in the early 1980s when the first works appeared on the application of control theory in models of pharmacokinetics and pharmacodynamics for antitumor therapies. Forty years after those first works, the theory of control continues to be considered a mathematical analysis tool of extreme importance and usefulness, but the challenges it must overcome in order to manage the complexity of biological processes are in fact not yet overcome. In this article, we introduce the reader to the basic ideas of control theory, its aims and its mathematical formalization, and we review its use in cell phase-specific models for cancer chemotherapy. We discuss strengths and limitations of the control theory approach to the analysis pharmacokinetics and pharmacodynamics models, and we will see that most of them are strongly related to data availability and mathematical form of the model. We propose some future research directions that could prove useful in overcoming the these limitations and we indicate the crucial steps preliminary to a useful and informative application of control theory to cancer chemotherapy modeling.

Research on fuzzy symmetrical control of valve controlled asymmetric hydraulic cylinder system

In order to solve the problems, such as the asymmetry, complex control methods, inconsistent dynamic characteristics for positive/negative directions and poor stability for asymmetric control system, in this paper, a system symmetric control method based on state feedback was brought out and the state space mathematical model was derived for valve controlled hydraulic cylinder system. With the symmetric control method of the state feedback, the valve controlled asymmetric hydraulic system can be converted into state space symmetric system, then the unified control method can be used for positive and negative directions after conversion, finally the feedback link of the system was educed. Through simulation, the accuracy of the model and the effectiveness of the control method were verified. Through experiments, the input and output characteristics and load response characteristics of the system before and after conversion were compared. It was concluded that the system had symmetric characteristics for inputs and outputs, and better load response characteristics after conversion. This study can be a base for the application of symmetric control theory to large asymmetric hydraulic systems and was of great help to realize symmetric control of large asymmetric hydraulic systems.

The Evolution of Insulin Administration in Type 1 Diabetes.

Insulin has been utilized in the treatment of type 1 diabetes (T1D) for 100 years. While there is still no cure for T1D, insulin administration has undergone a remarkable evolution which has contributed to improvements in quality of life and life expectancy in individuals with T1D. The advent of faster-acting and longer-acting insulins allowed for the implementation of insulin regimens more closely resembling normal insulin physiology. These improvements afforded better glycemic control, which is crucial for limiting microvascular complications and improving T1D outcomes. Suspension of insulin delivery in response to actual and forecasted hypoglycemia has improved quality of life and mitigated hypoglycemia without compromising glycemic control. Advances in continuous glucose monitoring (CGM) and insulin pumps, efforts to model glucose and insulin kinetics, and the application of control theory to T1D have made the automation of insulin delivery a reality. This review will summarize the past, present, and future of insulin administration in T1D.

A new conceptual model to treat tourist behavior: Locus of control theory application

A new conceptual model to treat tourist behavior: Locus of control theory application

Representation, Incorporation, and Corrections Spending: The Counterbalancing Effect of Black Political Incorporation

AbstractTheories concerning the adoption of punitive policies at the state level often cite two dynamics: conservative ideology and racial threat, that punitive policies are more likely in states with Republican politicians and a higher proportion of Black residents. I argue these theories lose their explanatory power in the post-Civil Rights era, and suggest Black political incorporation acts as a powerful antidote to the punitive impulses of government officials. I test my hypotheses on a dataset of state corrections spending from 1983 to 2011 and find evidence for the counterbalancing argument. States with increasing percentages of Black state legislators spend .36 fewer dollars per capita on corrections, suggesting Black political incorporation is an important mediator in the relationship between racial threat and corrections budgets. This paper has implications for the application of the social control theory as descriptive representation grows, but also for the study of the effect of minority politicians on budgets and policy more broadly. The adoption of policies deleterious to certain communities can be mitigated by the presence of representatives who legislate on behalf of those communities.

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing (part: 2)

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing (part: 2)

Solutions to the linear transpose matrix equations and their application in control

In this paper, we study the solutions to the linear transpose matrix equations $$AX+X^{T}B=C$$ and $$AX+X^{T}B=CY$$ , which have many important applications in control theory. By applying Kronecker map and Sylvester sum, we obtain some necessary and sufficient conditions for existence of solutions and the expressions of explicit solutions for the Sylvester transpose matrix equation $$AX+X^{T}B=C$$ . Our conditions only need to check the eigenvalue of $$ B^{T}A^{-1}$$ , and, therefore, are simpler than those reported in the paper (Piao et al. in J Frankl Inst 344:1056–1062, 2007). The corresponding algorithms permit the coefficient matrix C to be any real matrix and remove the limit of $$C=C^{T}$$ in Piao et al. Moreover, we present the solvability and the expressions of parametric solutions for the generalized Sylvester transpose matrix equation $$AX+X^{T}B=CY$$ using an alternative approach. A numerical example is given to demonstrate that the introduced algorithm is much faster than the existing method in the paper (De Teran and Dopico in 434:44–67;2011). Finally, the continuous zeroing dynamics design of time-varying linear system is provided to show the effectiveness of our algorithm in control.

Do Social Bonds Matter? Social Control Theory and Its Relationship to Desistance From Substance Abuse in China

This study examines the effects of social bonds on drug users’ desistance from substance abuse, with a special focus on testing the applicability of social control theory in the context of China. Using data from a sample of 419 Chinese drug users, this study reveals salient influences of such bonding variables as familial attachment, involvement, belief, and parenthood on drug users’ confidence and efforts in achieving abstinence, providing some support for the arguments of social control theory. Given the limitations of institutional response in dealing with substance abuse issues, these findings have important policy implications for the direction of efforts to encourage desistance-related behavior among substance abusers.

Solving differential Riccati equations: A nonlinear space-time method using tensor trains

Differential Riccati equations are at the heart of many applications in control theory. They are time-dependent, matrix-valued, and in particular nonlinear equations that require special methods for their solution. Low-rank methods have been used heavily for computing a low-rank solution at every step of a time-discretization. We propose the use of an all-at-once space-time solution leading to a large nonlinear space-time problem for which we propose the use of a Newton–Kleinman iteration. Approximating the space-time problem in a higher-dimensional low-rank tensor form requires fewer degrees of freedom in the solution and in the operator, and gives a faster numerical method. Numerical experiments demonstrate a storage reduction of up to a factor of 100.

Refined Upper Solution Bound of the Continuous Coupled Algebraic Riccati Equation

The continuous coupled algebraic Riccati equation (CCARE) has wide applications in control theory and linear systems. In this paper, by a constructed positive semidefinite matrix, matrix inequalities, and matrix eigenvalue inequalities, we propose a new two-parameter-type upper solution bound of the CCARE. Next, we present an iterative algorithm for finding the tighter upper solution bound of CCARE, prove its boundedness, and analyse its monotonicity and convergence. Finally, corresponding numerical examples are given to illustrate the superiority and effectiveness of the derived results.

Robust Two-degree-of-freedom Control Based on H∞ Method for PMSM Drive System

Background: The conventional method using one-degree-of-freedom (1DOF) controller for Permanent Magnet Synchronous Motor (PMSM) servo system has the trade-off problem between the dynamic performance and the robustness. Methods: In this paper, by using H∞ control theory, a novel robust two-degree-of-freedom (2DOF) controller has been proposed to improve the position control performance of PMSM servo system. Using robust control theory and 2DOF control theory, a H∞ robust position controller has been designed and discussed in detail. Results: The trade-off problem between the dynamic performance and robustness which exists in one-degree-of-freedom (1DOF) control can be dealt with by the application of 2DOF control theory. Then, through H∞ control theory, the design of robust position controller can be translated to H∞ robust standard design problem. Moreover, the control system with robust controller has been proved to be stable. Conclusion: Further simulation results demonstrate that compared with the conventional PID control, the designed control system has better robustness and attenuation to the disturbance of load impact.