Application Of Control Theory Research Articles

Homeostasis: The Underappreciated and Far Too Often Ignored Central Organizing Principle of Physiology.

The grand challenge to physiology, as was first described in an essay published in the inaugural issue of Frontiers in Physiology in 2010, remains to integrate function from molecules to intact organisms. In order to make sense of the vast volume of information derived from, and increasingly dependent upon, reductionist approaches, a greater emphasis must be placed on the traditional integrated and more holistic approaches developed by the scientists who gave birth to physiology as an intellectual discipline. Our understanding of physiological regulation has evolved over time from the Greek idea of body humors, through Claude Bernard’s “milieu intérieur,” to Walter Cannon’s formulation of the concept of “homeostasis” and the application of control theory (feedback and feedforward regulation) to explain how a constant internal environment is achieved. Homeostasis has become the central unifying concept of physiology and is defined as a self-regulating process by which an organism can maintain internal stability while adjusting to changing external conditions. Homeostasis is not static and unvarying; it is a dynamic process that can change internal conditions as required to survive external challenges. It is also important to note that homeostatic regulation is not merely the product of a single negative feedback cycle but reflects the complex interaction of multiple feedback systems that can be modified by higher control centers. This hierarchical control and feedback redundancy results in a finer level of control and a greater flexibility that enables the organism to adapt to changing environmental conditions. The health and vitality of the organism can be said to be the end result of homeostatic regulation. An understanding of normal physiology is not possible without an appreciation of this concept. Conversely, it follows that disruption of homeostatic mechanisms is what leads to disease, and effective therapy must be directed toward re-establishing these homeostatic conditions. Therefore, it is the purpose of this essay to describe the evolution of our understanding of homeostasis and the role of physiological regulation and dysregulation in health and disease.

Government policy as a key moderator to contractors’ risk attitudes among Malaysian construction companies

Government policy as a key moderator to contractors’ risk attitudes among Malaysian construction companies

Application of control theory in a delayed-infection and immune-evading oncolytic virotherapy.

Oncolytic virotherapy is a promising cancer treatment that harnesses the power of viruses. Through genetic engineering, these viruses are cultivated to infect and destroy cancer cells. While this therapy has shown success in a range of clinical trials, an open problem in the field is to determine more effective perturbations of these viruses. In this work, we use a controlled therapy approach to determine the optimal treatment protocol for a delayed infection from an immune-evading, coated virus. We derive a system of partial differential equations to model the interaction between a growing tumour and this coated oncolytic virus. Using this system, we show that viruses with inhibited viral clearance and infectivity are more effective than uncoated viruses. We then consider a hierarchical level of coating that degrades over time and determine a nontrivial initial distribution of coating levels needed to produce the lowest tumour volume. Interestingly, we find that a bimodal mixture of thickly coated and thinly coated virus is necessary to achieve a minimum tumour size. Throughout this article we also consider the effects of immune clearance of the virus. We show how different immune responses instigate significantly different treatment outcomes.

Solving coupled tensor equations via higher order LSQR methods

Tensors have a wide application in control theory, data mining, chemistry, information sciences, documents analysis and medical engineering. The material here is motivated by the development of the efficient numerical methods for solving the coupled tensor equations (A1*M X *N B1 + C1 *M Y *N D1 = E1, A2 *M X *N B2 + C2 *M Y *N D2 = E2, with Einstein product. We propose the tensor form of the LSQR methods to find the solutions X and Y of the coupled tensor equations. Finally we give some numerical examples to illustrate that our proposed methods are able to accurately and efficiently find the solutions of tensor equations with Einstein product.

Social bonds in the diaspora: The application of social control theory to somali refugee young adults in resettlement.

Social bonds in the diaspora: The application of social control theory to somali refugee young adults in resettlement.

Application of optimal control theory on optimal advertising expenditure in monopoly

Presented paper is being focused on Optimal control theory, Variation Calculus and its economic application. Aim of this research paper is to shortly describe Optimal control and Variation Calculus and to present how can we deal with these type of issues. The last part of this paper is presenting possible economic application of Optimal control, based on the maximization of profit in monopoly while introducing new product on the market. Our control variable is the advertising rate, which affects the profit of monopoly through advertising expenditures and as a state variable was the market share defined.

Water System Examples for Control Education

Abstract Management of water systems is becoming more and more complex; this creates opportunities for the application of control theory. These opportunities are the subject of a course on operational water management given to students of the water management department, Delft University of Technology, over the past 15 years. Traditional examples in control theory courses are taken from industry and do not easily map to water systems, so examples were developed that use water systems to illustrate control theory concepts. This provided the students with a link between control theory and water management practice.

Kontrol Optimal Upaya Pengobatan Penyakit Campak Menggunakan Model Endemi SIR

Measles is an acute highly contagious disease caused by Paramyxovirus. Measles is considered as a dangerous disease because it cause complications, brain and other organs damage, lifelong disability, paralysis and even death. In the previous studies, it was known that the spread of measles highly dependent on number of infected individuals so it is necessary to control measles through treatment. In this paper, we study about the application of the optimal control theory on the system of differential equations of the SIR endemic model. Determination of the optimal control is obtained through the application of the Pontryagin minimum principle. The main target in this paper is to find a unique optimal control where the optimal control can be described as an efficiency rate of treatment in individuals infected with measles to decrease the number of infected individuals.

Asymptotic evaluation of the state and stiffness of the van der Paul oscillator

In many applications of physics, biology, and other sciences, an approach based on the concept of model equations is used as an approximate model of complex nonlinear processes. The basis of this concept is the provision that a small number of characteristic types movements of simple mathematical models inherent in systems gives the key to understanding and exploring a huge number of different phenomena. With this approach it is a priori assumed that the entire physical diverseness can be represented in the form of fairly simple model equations. It is contributes to a qualitative study of complex systems for various physical nature since basic models individually are well studied, their parameters have a physical interpretation. In particular, it is well known that oscillatory motion of various systems with a stable limit cycle can be modeled by a system consisting of one or more coupled van der Pol oscillators. Such systems are widely represented in various technical devices and in the study and modeling of some biological functions of the body, such as cardiac activity, respiration, locomotor activity, etc. It is considered a typical situation for many practical applications of control theory when the complete state vector of the system is unknown and only some of the functions of the state variables -- the outputs of the system are accessible to measurement. Therefore, the problem of determining in real time the state and parameters of such systems based on the results of measuring the output signals are relevant. One of these inverse control problems, namely, the problem of observability and parameter identification of an model oscillatory system is considered in this article. For observation and identification scheme design the method of invariant relations developed in analytical mechanics is used. Its modification in control problems allows us to synthesize additional relationships between known and unknown quantities of a dynamical system that arise during the observed motion. The method does not involve linearization of the original system and is essentially non-linear. The constructed nonlinear observer provides an asymptotic estimation of unknown parameter and velocity of oscillations.

On linear quadratic optimal control of discrete‐time complex‐valued linear systems

SummaryWe study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete‐time complex‐valued linear systems, which have several potential applications in control theory. Firstly, an iterative algorithm was proposed to solve the discrete‐time bimatrix Riccati equation associated with the LQR problem. It is shown that the proposed algorithm converges to the unique positive definite solution (bimatrix) to the bimatrix Riccati equation with appropriate initial conditions. With the help of this iterative algorithm, the LQR problem for the antilinear system, which is a special case of complex‐valued linear system, was carefully examined and three different Riccati equations–based approaches were provided, namely, bimatrix Riccati equation, anti‐Riccati equation, and normal Riccati equation. The established approach is then used to solve the LQR problem for a discrete‐time time‐delay system with one‐step state delay, and a numerical example was used to illustrate the effectiveness of the proposed methods.

Robust analysis for premium-reserve models in a stochastic nonlinear discrete-time varying framework

The effective management of uncertainty and complexity in premium pricing and reserve accumulation processes provide new challenges to the decision- and policy-makers. In this regard, the implementation of complex mathematical tools and advanced statistical techniques is highly acquired. Over the last three decades, methodologies and applications of robust control theory to finance and economics have received strong attention among researchers and practitioners. However, relatively scant research has been carried out so far in relation to insurance. This paper proposes a stochastic, nonlinear time-varying premium-reserve (P-R) system with Lipschitz-type conditions in discrete-time to explore P-R system’s stability, stabilization and H∞-control properties. In our case, as an extension of the classical quadratic condition, the one-side Lipschitz conditions are also considered and a nonconvex feasibility problem is formulated and solved. In addition, both robust stochastic stability and a pre-specified disturbance attenuation level can be guaranteed. Finally, numerical examples are presented to illustrate the applicability of theoretical treatment.

Recent advances in optimization and game theoretic control for networked systems

AbstractThe aim of this paper is to provide an overview, although unnecessarily complete, of recent advances in optimal control, optimization, and game theory for networked systems. First, the recent research results and progress in optimal control and game theory for logical domain networked systems are summarized. Then, the recent developments on networked optimization and game theory for continuous domain systems are presented afterward. Finally, after introducing some recent practical applications of optimal control and game theory on networked systems, we conclude the paper with a short discussion on future research perspectives.

Application of Control Theory to Describe the Management of the Regional Socio-Economic System

Application of Control Theory to Describe the Management of the Regional Socio-Economic System

Supplemental Material for Social Bonds in the Diaspora: The Application of Social Control Theory to Somali Refugee Young Adults in Resettlement

Supplemental Material for Social Bonds in the Diaspora: The Application of Social Control Theory to Somali Refugee Young Adults in Resettlement

Robust Analysis for Premium-Reserve Models in a Stochastic Nonlinear Discrete-Time Varying Framework

The effective management of uncertainty and complexity in premium pricing and reserve accumulation processes provide new challenges to the decision- and policy- makers. In this regard, the implementation of complex mathematical tools and advanced statistical techniques is highly acquired. Over the last three decades, methodologies and applications of robust control theory to finance and economics have received strong attention among researchers and practitioners. However, relatively scant research has been carried out so far in relation to insurance. This paper proposes a stochastic, nonlinear time-varying premium-reserve (P-R) system with Lipschitz- type conditions in discrete-time to explore P-R system’s stability, stabilisation and Hoo-control properties. In our case, as an extension of the classical quadratic condition, the one-side Lipschitz conditions are also considered and a nonconvex feasibility problem is formulated and solved. In addition, both robust stochastic stability and a pre-specified disturbance attenuation level can be guaranteed. Finally, numerical examples are presented to illustrate the applicability of theoretical treatment.

Expression of a Real Matrix as a Difference of a Matrix and its Transpose Inverse

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of transpose-inverse terms prove to be obstacles, particularly in control theory and related applications such as computational simulation and analysis of matrix representations of articulated figures.

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

Automatic controls refer to the application of control theory to regulate systems or processes without human intervention, and the notion is often usefully applied to space applications. A key part of controlling flexible space robotics is the control-structures interaction of a light, flexible structure whose first resonant modes lie within the bandwidth of the controller. In this instance, the designed-control excites the problematic resonances of the highly flexible structure. This manuscript reveals a novel compensator capable of minimum-time performance of an in-plane maneuver with zero residual vibration (ZV) and zero residual vibration-derivative (ZVD) at the end of the maneuver. The novel compensator has a whiplash nature of first commanding maneuver states in the opposite direction of the desired end state. For a flexible spacecraft simulator (FSS) free-floating planar robotic arm, this paper will first derive the model of the flexible system in detail from first principles. Hamilton’s principle is augmented with the adjoint equation to produce the Euler–Lagrange equation which is manipulated to prove equivalence with Newton’s law. Extensive efforts are expended modeling the free–free vibration equations of the flexible system, and this extensive modeling yields an unexpected control profile—a whiplash compensator. Equations of motion are derived using both the Euler–Lagrange method and Newton’s law as validation. Variables are then scaled for efficient computation. Next, general purposed pseudospectral optimization software is used to seek an optimal control, proceeding afterwards to validate optimality via six theoretical optimization necessary conditions: (1) Hamiltonian minimization condition; (2) adjoint equations; (3) terminal transversality condition; (4) Hamiltonian final value condition; (5) Hamiltonian evolution equation; and lastly (6) Bellman’s principle. The results are novel and unique in that they initially command full control in the opposite direction from the desired end state, while no such results are seen using classical control methods including classical methods augmented with structural filters typically employed for controlling highly flexible multi-body systems. The manuscript also opens an interesting question of what to declare when the six optimality necessary conditions are not necessarily in agreement (we choose here not to declare finding the optimal control, instead calling it suboptimal).

Control of Black-Box Embedded Systems by Integrating Automaton Learning and Supervisory Control Theory of Discrete-Event Systems

The paper presents an approach to the control of black-box embedded systems by integrating automaton learning and supervisory control theory (SCT) of discrete-event systems (DES), where automaton models of both the system and requirements are unavailable or hard to obtain. First, the system is tested against the requirements. If all the requirements are satisfied, no supervisor is needed and the process terminates. Otherwise, a supervisor is synthesized to enforce the system to satisfy the requirements. To apply SCT and automaton learning technologies efficiently, the system is abstracted to be a finite-discrete model. Then, a $C^{*}$ learning algorithm is proposed based on the classical $L^{*}$ algorithm to infer a Moore automaton describing both the behavior of the system and the conjunctive behavior of the system and the requirements. Subsequently, a supervisor for the system is derived from the learned Moore automaton and patched on the system. Finally, the controlled system is tested again to check the correctness of the supervisor. If the requirements are still not satisfied, a larger Moore automaton is learned and a refined supervisor is synthesized. The whole process iterates until the requirements hold in the controlled system. The effectiveness of the proposed approach is manifested through two realistic case studies. Note to Practitioners —Supervisory control theory of DES can synthesize maximally permissive supervisory controllers to ensure the correctness of software-controlled processes. The application of supervisory control theory relies on automaton models of the plant and specifications; however, the required models are often unavailable and difficult to obtain for black-box embedded systems. Automaton learning is an effective method for inferring models of black-box systems. This paper integrates the two technologies so that the supervisory control theory is applicable to the development of black-box embedded software systems. The proposed approach is implemented in a toolchain that connects automaton learning algorithms, SCT, and testing algorithms via scripts. The obtained supervisor is implemented as a software patch to monitor and control the original system online.

On a more general fractional integration by parts formulae and applications

The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators; thus, we develop fractional integration by parts for fractional integrals, Riemann–Liouville, Liouville–Caputo, Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. We allow the left and right fractional integrals of order α>0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case α=1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution.

A controller synthesis framework for automated service composition

Nowadays, Web services allow interoperability among distributed software applications deployed on different platforms and architectures which in effect plays a major role in electronic businesses. Web services allow organizations to carry out certain business activities automatically and in a distributed fashion. However, in some circumstances, a single service is not able to perform a certain task and it becomes imperative to compose two or more services in order to complete it. Thus, a key research challenge in this field is the problem of automatic service composition. Several approaches exist that tackle the problem of automatic service composition, however, the task of generating provably correct Web service compositions still remains a challenging and complex task. In this paper, we develop a formal framework for modeling Web service compositions based on Supervisory Control Theory (SCT) of discrete-event systems. We model services that exchange messages and exhibit nondeterministic behaviours. The objective is to synthesize a supervisor which interacts with a given set of Web services through messages to guarantee that a given specification is satisfied. A key novelty of this work is the application of control theory to service-oriented computing and the incorporation of run-time input into the supervisor generation process. First, we describe a novel supervisory control framework for automated composition of Web services. The framework employs Labelled Transition Systems equipped with guards and data variables to model Web services and provides a technique to synthesize a controller. We model the interactions of services asynchronously and we use the guards and data variables to allow us to express certain preconditions which are then propagated from the system requirements through the overall composite service. Second, we develop a set of algorithms to generate a controller satisfying a given functional requirement also specified as a Labelled Transition System equipped with guards and data variables. Besides the standard disabling and enabling of events, the generated controller in our framework has the ability to enforce certain events based on run-time information to drive the system towards its goal. In addition, the controller is able to impose restrictions on the kind of data that can be sent or received by services. This includes the automatic generation of stronger guards or preconditions which impose restrictions on which path to take during execution. Lastly, we state a theorem capturing the existence of a controller and provide a proof to demonstrate the correctness of the proposed approach.