In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. The performance index of a (FOCP) is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in details.
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency of the resulting approximations related to the original infinite-dimensional optimization problem and leads to specific implementable algorithms.
A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction and dissipative system. Mild solution for bioheat transfer equation and its adjoint problem are proposed. Controllability and exponentially stability for the related system is proved. The optimal control problem is solved using strongly continuous semigroup solution and time discretization. Mathematical simulations for a thermal therapy in the presence of point heating power are presented to investigate efficiency of the proposed technique.
GPS (Global Positioning System) technique has become a major tool in contemporary surveying and geodesy. This concerns mostly measurements of horizontal point coordinates, where centimeter-level accuracies are usually required and easily achievable. For the height component, however, these requirements are higher and millimeter-level accuracy is necessary. On the other hand, the intrinsic precision of GPS-derived heights is clearly lower comparing to the horizontal components. This is due to unfavorable satellite geometry, adverse effects of the troposphere or GPS antenna phase center offset and variations. In order to overcome these effects one has to carefully model all the error sources and rigorously process the GPS data. This paper presents studies on the optimal GPS data processing strategy suitable for precise leveling. This was done through the extensive testing and selection of the most appropriate observational session duration, ambiguity resolution strategy, network geometry, troposphere and ionospheric delay reduction methods, signal linear co mbination, elevation angle cut-off, etc. The analyzed processing strategies were evaluated through the processing of a test network. The test network consisted of 19 monitored points and 5 control points, and covered the area of 20 km x 60 km. The obtained results show that the precise GPS leveling with the selected optimal processing strategy allows for about 3 mm repeatability of height measurements when processing 4-hour long sessions. In our opinion GPS leveling may serve as fast and cost-effective replacement of classic geometric leveling, especially in applications where the hei ghts in orthometric or normal height systems are not necessary. This is the case in, e.g., ground deformation studies., Katarzyna Stepniak, Radosław Baryła, Paweł Wielgosz and Grzegorz Kurpinski., and Obsahuje bibliografické odkazy
Fuzzy logic, neural network, fuzzy-neural networks play an important role in the linguistic modeling of intelligent control and decision making in complex systems. The Fuzzy-Neural Network (FNN) learning represents one of the most effective algorithms to build such linguistic models. This paper proposes an Artificial Immune Algorithm (AIA) based optimal learning fuzzy-neural network (IM-FNN). The proposed learning scheme includes the discovery of the fuzzy-neural network structure which can handle linguistic knowledge and the tuning of the membership function of the fuzzy inference system is achieved by AIA. The learning algorithm of the IM-FNN is composed of two phases. The first phase is to find the initial membership functions of the fuzzy neural network model. In the second phase, immune algorithm is used for tuning the membership functions of the proposed model. This paper also suggests techniques in determining the values of the steady-state equivalent circuit parameters of a three-phase squirrel-cage induction machine using immune algorithm.
So far, great efforts have been made to understand the demands
of extremely premature neonates (EPNs´; born before
the 28th week of gestation) on postnatal care, including optimal
oxygen saturation, that will allow them to survive without disability.
A major yet unresolved problem is to find an “optimal range” of
their oxygen saturation and to maintain it without drops or
increases, i.e., without hypoxia or hyperoxia. The individual
sections of this paper deal with the changes of SpO2 (an estimate
of SaO2 measured by pulse oximetry) that occur before, during,
and after premature labor, postnatal factors affecting SpO2, and
especially how to find an acceptable compromise in choosing the
most effective and minimally harmful range of SpO2 for EPNs’ with
the careful FiO2 adjustment and continually monitored SpO2. At
present, the two SpO2 ranges, narrow (90-94 %) vs. wider
(88-94 %), are most discussed. However, the question of how
much oxygen is too much or little remains unanswered. There is
even a view that there is no uniform optimal SpO2 range for EPNs,
and that each newborn has its own, individually specific range that
changes due to its intrinsic and/or extrinsic factors.
Positive Position Feedback (PPF) is one of the most attractive vibration control method due to its stability and ease of implementation. On the other hand, low robustness makes the PPF design more complicated in multimodal control case. It is known that a little change in optimal parameters setup, especially the change in controller frequency, can strongly degrade the control effort. Thus knowing a good approximation of optimal PPF parameters can be very helpful in practical implementations and simplified analytical relations between optimal parameters and modal properties of the structure are inevitable for efficient control design. In this paper derivation of such relations is introduced, based on simplified transfer function of controlled structure. Furthermore influence of the parallel PPF controllers in multimodal vibration suppression is analyzed and formulae for optimal parameters updating are suggested. Optimal multimodal PPF control design is demonstrated on experimental example of vibration suppression of beam structure. and Obsahuje seznam literatury
Introduction: The type of the preparation junction is determined by a number of factors that need to be taken in consideration with CAD/CAM Fixed Prosthodontics: the material of which the construction will be made; the type and condition of the retainer teeth, of their periodontium and the occlusion; the design software, the CAM setting and the type of drills; the working protocol; the type of the cement and the method of cementation. Purpose: The aim of this publication is to describe the optimal preparation junctions for all-ceramic crown and bridge restorations made by CAM 5 - S 2 Impression, VHF. Materials and methods: Suitable are chamfer and shoulder preparation junction with rounded inner angle (width 1 - 1, 5 mm). Trimming of 1.5 – 2 mm dental tissues is necessary on the occlusal surface. The homothetic reduction of teeth is optimal. Results and discussion: The width depends on the size and vitality of the tooth. In stained teeth and those built with metal pins the removal of more tissues provides a greater volume needed to disguise the dark color. Vestibular preparation under the level of the gingiva is preferable to ensure optimal aesthetics. Preparation junction is determined also by the CAD/CAM technology - the type of drills and protocol of impression taking (classical or digital). The creation of a working model with TRIOS, 3Shape intraoral scanner is greatly facilitated by preparation junctions made above the gingival margin. Conclusion: Knowledge about the criteria for selection the preparation junctions is essential for fabrication accurate and aesthetic CAD/CAM restorations., Angelina Vlahova,Viktor Hadzhigaev, Christo Kissov, Rada Kazakova,Tanya Bozhkova, and Literatura