Mathematical aspects of descriptive and optimization controlled systems models design

Запропоновано підходи до специфікації дескриптивних моделей динамічних систем з невідомими та відомими вхідними сигналами. Розроблено алгоритми ідентифікації з високими імітаційними та прогнозними властивостями. Представлено принцип переходу від дескриптивних до оптимізаційних моделей (динамічних та статичних). Всі підходи апробовані на реальних статистичних даних еволюції макроекономічної системи відкритого типу. Результати чисельного експерименту продемонстрували високу точність, адекватність та практичну цінність побудованих моделей. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/8183Предложен подход к спецификации дескриптивных моделей динамических систем с неизвестными и известными входными сигналами. Разработаны алгоритмы идентификации с высокими имитационными и прогнозными свойствами. Представлен принцип перехода от дескриптивных к оптимизационным моделям (динамическим и статическим). Все подходы апробированы на реальных статистических данных эволюции макроэкономической системы открытого типа. Результаты численного эксперимента продемонстрировали высокую точность, адекватность и практическую ценность построенных моделей. При цитировании документа, используйте ссылку http://essuir.sumdu.edu.ua/handle/123456789/8183An approach to specification of dynamic systems descriptive models with unknown and known inputs has been proposed. The identification algorithms with high simulation and forecast properties have been developed. The principle of transition from descriptive to optimization (dynamic and static) models has been presented. All approaches has been approbated using real statistical dataset of the open macroeconomic system evolution. The results of numerical experiment have confirmed the high accuracy, adequacy and practical significance of the constructed models. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/818

Modeling and Analysis of Power Processing Systems (MAPPS). Volume 1: Technical report

Computer aided design and analysis techniques were applied to power processing equipment. Topics covered include: (1) discrete time domain analysis of switching regulators for performance analysis; (2) design optimization of power converters using augmented Lagrangian penalty function technique; (3) investigation of current-injected multiloop controlled switching regulators; and (4) application of optimization for Navy VSTOL energy power system. The generation of the mathematical models and the development and application of computer aided design techniques to solve the different mathematical models are discussed. Recommendations are made for future work that would enhance the application of the computer aided design techniques for power processing systems

Human-in-the-Loop Model Predictive Control of an Irrigation Canal

Until now, advanced model-based control techniques have been predominantly employed to control problems that are relatively straightforward to model. Many systems with complex dynamics or containing sophisticated sensing and actuation elements can be controlled if the corresponding mathematical models are available, even if there is uncertainty in this information. Consequently, the application of model-based control strategies has flourished in numerous areas, including industrial applications [1]-[3].Junta de Andalucía P11-TEP-812

Active control of buckling of flexible beams

The feasibility of using the rapidly growing technology of the shape memory alloys actuators in actively controlling the buckling of large flexible structures is investigated. The need for such buckling control systems is becoming inevitable as the design trends of large space structures have resulted in the use of structural members that are long, slender, and very flexible. In addition, as these truss members are subjected mainly to longitudinal loading they become susceptible to structural instabilities due to buckling. Proper control of such instabilities is essential to the effective performance of the structures as stable platforms for communication and observation. Mathematical models are presented that simulate the dynamic characteristics of the shape memory actuator, the compressive structural members, and the associated active control system. A closed-loop computer-controlled system is designed, based on the developed mathematical models, and implemented to control the buckling of simple beams. The performance of the computer-controlled system is evaluated experimentally and compared with the theoretical predictions to validate the developed models. The obtained results emphasize the importance of buckling control and suggest the potential of the shape memory actuators as attractive means for controlling structural deformation in a simple and reliable way

Model of large scale man-machine systems with an application to vessel traffic control

Mathematical models are discussed to deal with complex large-scale man-machine systems such as vessel (air, road) traffic and process control systems. Only interrelationships between subsystems are assumed. Each subsystem is controlled by a corresponding human operator (HO). Because of the interaction between subsystems, the HO has to estimate the state of all relevant subsystems and the relationships between them, based on which he can decide and react. This nonlinear filter problem is solved by means of both a linearized Kalman filter and an extended Kalman filter (in case state references are unknown and have to be estimated). The general model structure is applied to the concrete problem of vessel traffic control. In addition to the control of each ship, this involves collision avoidance between ship

On stabilization of nonlinear systems with drift by time-varying feedback laws

This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie brackets of length up to 3. This class of systems includes, in particular, mathematical models of rotating rigid bodies. We propose an explicit control design scheme with time-varying trigonometric polynomials whose coefficients depend on the state of the system. The above coefficients are computed in terms of the inversion of the matrix appearing in the controllability condition. It is shown that the proposed controllers can be used to solve the stabilization problem by exploiting the Chen-Fliess expansion of solutions of the closed-loop system. We also present results of numerical simulations for controlled Euler's equations and a mathematical model of underwater vehicle to illustrate the efficiency of the obtained controllers.Comment: This is the author's version of the manuscript accepted for publication in the Proceedings of the 12th International Workshop on Robot Motion Control (RoMoCo'19

Theoretical prediction of drug release in GI tract from spherical matrix systems

The significance of controlled release drug delivery systems (CRDDS) lies in their ability to deliver the drug at a steady rate thus reducing the dosage interval and providing a prolonged pharmacodynamic effect. But despite the steadily increasing practical importance of these devices, little is known regarding their underlying drug release mechanisms. Mathematical modeling of these drug delivery systems could help us understand the underlying mass transport mechanisms involved in the control of drug release. Mathematical modeling also plays an important role in providing us with valuable information such as the amount of drug released during a certain period of time and when the next dosage needs to be administered. Thus, potentially reducing the number of in-vitro and in-vivo experiments which in some cases are infeasible. There is a large spectrum of published mathematical models for predicting drug release from CRDDS in vitro following conventional approaches. These models describe drug release from various types of controlled delivery devices for perfect sink conditions. However in a real system (human body) a sink condition may not be applicable. For a CRDDS along with the physiochemical properties (solubility, diffusion, particle size, crystal form etc.) the physiological factors such as gastrointestinal tract (GI) pH, stomach emptying, (GI) motility, presence of food, elimination kinetics etc., also affect the rate of drug release. As the drug delivery system is expected to stay in the human body for a longer period of time when compared to a immediate release dosage form the process of drug release occurs in conjunction with the absorption (for oral delivery systems) and elimination kinetics. Earlier work by Ouruemchi et.al.[71] include prediction of the plasma drug concentration for an oral diffusion controlled drug delivery system. Amidon et.al.[68] developed several models for predicting the amount of drug absorbed within through the intestine walls for immediate release dosage forms. However none of these models study the effect of absorption rate on the rate of drug release for an oral controlled drug delivery system. In this work mathematical models are developed for prediction of drug release from both diffusion controlled and dissolution controlled drug delivery systems taking into account the affect of absorption rate. Spherical geometry of the particles is considered. The model is developed by assuming that the drug is release into a finite volume and is thereby absorbed through the intestine wall following first order kinetics. A closed form solution is obtained for the prediction of fraction of drug released for a diffusion controlled drug delivery system. The results are compared with both experimental data (taken from literature) as well as existing models in the literature. Whereas for a dissolution-diffusion controlled drug delivery system non linear dissolution kinetics are taken into consideration and the problem is solved by both numerical and analytical techniques. In addition two simple models are also presented for dissolution controlled drug delivery devices