Search results for: joint optimization

Authors: D. Kaczorek

Abstract:

Internal insulation of external walls is often problematic due to increased moisture content in the wall and interstitial or surface condensation risk. In this paper, the hygrothermal performance of prefabricated, concrete, large panel, external wall typical for WK70 system, commonly used in Poland in the 70’s, with inside, additional insulation was investigated. Thermal insulation board made out of hygroscopic, natural materials with moisture buffer capacity and extruded polystyrene (EPS) board was used as interior insulation. Experience with this natural insulation is rare in Poland. The analysis was performed using WUFI software. First of all, the impact of various standard boundary conditions on the behavior of the different wall assemblies was tested. The comparison of results showed that the moisture class according to the EN ISO 13788 leads to too high values of total moisture content in the wall since the boundary condition according to the EN 15026 should be usually applied. Then, hygrothermal 1D-simulations were conducted by WUFI Pro for analysis of internally added insulation, and the weak point like the joint of the wall with the concrete ceiling was verified using 2D simulations. Results showed that, in the Warsaw climate and the indoor conditions adopted in accordance with EN 15026, in the tested wall assemblies, regardless of the type of interior insulation, there would not be any problems with moisture - inside the structure and on the interior surface.

Keywords: Concrete large panel wall, hygrothermal simulation, internal insulation, moisture related issues.

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Authors: A. Diaf, H. Aburideh, Z.Tigrine, D. Tassalit, F.Alaoui

Abstract:

The tray/multi-tray distillation process is a topic that has been investigated to great detail over the last decade by many teams such as Jubran et al. [1], Adhikari et al. [2], Mowla et al. [3], Shatat et al. [4] and Fath [5] to name a few. A significant amount of work and effort was spent focusing on modeling and/simulation of specific distillation hardware designs. In this work, we have focused our efforts on investigating and gathering experimental data on several engineering and design variables to quantify their influence on the yield of the multi-tray distillation process. Our goals are to generate experimental performance data to bridge some existing gaps in the design, engineering, optimization and theoretical modeling aspects of the multi-tray distillation process.

Keywords: Distillation, Desalination, Multi-Stage still, Solar Energy

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Authors: Miodrag T. Manić, Dejan I. Tanikić, Miloš S. Stojković, Dalibor M. ðenadić

Abstract:

The design of technological procedures for manufacturing certain products demands the definition and optimization of technological process parameters. Their determination depends on the model of the process itself and its complexity. Certain processes do not have an adequate mathematical model, thus they are modeled using heuristic methods. First part of this paper presents a state of the art of using soft computing techniques in manufacturing processes from the perspective of applicability in modern CAx systems. Methods of artificial intelligence which can be used for this purpose are analyzed. The second part of this paper shows some of the developed models of certain processes, as well as their applicability in the actual calculation of parameters of some technological processes within the design system from the viewpoint of productivity.

Keywords: fuzzy logic, manufacturing, neural networks

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Authors: A. Hossain, A. S. W. Kurny

Abstract:

The factors necessary to obtain an optimal heat treatment that influence the hardness and resistivity of Al-6Si-0.5Mg casting alloys with Cu or/and Ni additions were investigated. The alloys were homogenised (24hr at 500^oC), solutionized (2hr at 540^oC) and artificially ageing at various times and temperatures. The alloys were aged isochronally for 60 minutes at temperatures up to 400^oC and isothermally at 150, 175, 200, 225, 250 & 300^oC for different periods in the range 15 to 360 minutes. The hardness and electrical resistivity of the alloys were measured for various artificial ageing times and temperatures. From the isochronal ageing treatment, hardness found maximum ageing at 225^oC. And from the isothermal ageing treatment, hardness found maximum for 60 minutes at 225^oC. So the optimal heat treatment consists of 60 minutes ageing at 225^oC.

Keywords: Ageing, Al-Si-Mg alloy, hardness, resistivity.

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Authors: Asadollah Boshra, Ahmad Seif, Mehran Aghaei

Abstract:

A model of (4, 4) single-walled boron-nitride nanotube as a representative of armchair boron-nitride nanotubes studied. At first the structure optimization performed and then Nuclear Magnetic Resonance parameters (NMR) by Density Functional Theory (DFT) method at 11B and 15N nuclei calculated. Resulted parameters evaluation presents electrostatic environment heterogeneity along the nanotube and especially at the ends but the nuclei in a layer feel the same electrostatic environment. All of calculations carried out using Gaussian 98 Software package.

Keywords: Boron-nitride nanotube, Density Functional Theory, Nuclear Magnetic Resonance (NMR).

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Authors: Leehter Yao, Chin-Chin Lin

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A novel method of learning complex fuzzy decision regions in the n-dimensional feature space is proposed. Through the fuzzy decision regions, a given pattern's class membership value of every class is determined instead of the conventional crisp class the pattern belongs to. The n-dimensional fuzzy decision region is approximated by union of hyperellipsoids. By explicitly parameterizing these hyperellipsoids, the decision regions are determined by estimating the parameters of each hyperellipsoid.Genetic Algorithm is applied to estimate the parameters of each region component. With the global optimization ability of GA, the learned decision region can be arbitrarily complex.

Keywords: Ellipsoid, genetic algorithm, decision regions, classification.

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Authors: N. Rezaee, M Nayeripour, A. Roosta, T. Niknam

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With the prevalence of computer and development of information technology, Geographic Information Systems (GIS) have long used for a variety of applications in electrical engineering. GIS are designed to support the analysis, management, manipulation and mapping of spatial data. This paper presents several usages of GIS in power utilities such as automated route selection for the construction of new power lines which uses a dynamic programming model for route optimization, load forecasting and optimizing planning of substation-s location and capacity with comprehensive algorithm which involves an accurate small-area electric load forecasting procedure and simulates the different cost functions of substations.

Keywords: Geographic information systems (GIS), optimallocation and capacity, power distribution planning, route selection, spatial load forecasting.

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Authors: Young-Seok Choi

Abstract:

This paper presents a subband adaptive filter (SAF) for a system identification where an impulse response is sparse and disturbed with an impulsive noise. Benefiting from the uses of l1-norm optimization and l0-norm penalty of the weight vector in the cost function, the proposed l0-norm sign SAF (l0-SSAF) achieves both robustness against impulsive noise and much improved convergence behavior than the classical adaptive filters. Simulation results in the system identification scenario confirm that the proposed l0-norm SSAF is not only more robust but also faster and more accurate than its counterparts in the sparse system identification in the presence of impulsive noise.

Keywords: Subband adaptive filter, l0-norm, sparse system, robustness, impulsive interference.

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Authors: Zulhadi Zakaria, Nor Ashidi Mat Isa, Shahrel A. Suandi

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This paper reports the study results on neural network training algorithm of numerical optimization techniques multiface detection in static images. The training algorithms involved are scale gradient conjugate backpropagation, conjugate gradient backpropagation with Polak-Riebre updates, conjugate gradient backpropagation with Fletcher-Reeves updates, one secant backpropagation and resilent backpropagation. The final result of each training algorithms for multiface detection application will also be discussed and compared.

Keywords: training algorithm, multiface, static image, neural network

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Authors: Ali Al-Ataby , Fawzi Al-Naima

Abstract:

Symbolic Circuit Analysis (SCA) is a technique used to generate the symbolic expression of a network. It has become a well-established technique in circuit analysis and design. The symbolic expression of networks offers excellent way to perform frequency response analysis, sensitivity computation, stability measurements, performance optimization, and fault diagnosis. Many approaches have been proposed in the area of SCA offering different features and capabilities. Numerical Interpolation methods are very common in this context, especially by using the Fast Fourier Transform (FFT). The aim of this paper is to present a method for SCA that depends on the use of Wavelet Transform (WT) as a mathematical tool to generate the symbolic expression for large circuits with minimizing the analysis time by reducing the number of computations.

Keywords: Numerical Interpolation, Sparse Matrices, SymbolicAnalysis, Wavelet Transform.

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Authors: Hai-Qing Xie, Yun Zeng, Yong-Hong Yan, Guo-Liang Zhang, Tai-Hong Wang

Abstract:

We propose photo-BJMOSFET (Bipolar Junction Metal-Oxide-Semiconductor Field Effect Transistor) fabricated on SOI film. ITO film is adopted in the device as gate electrode to reduce light absorption. I-V characteristics of photo-BJMOSFET obtained in dark (dark current) and under 570nm illumination (photo current) are studied furthermore to achieve high photo-to-dark-current contrast ratio. Two variables in the calculation were the channel length and the thickness of the film which were set equal to six different values, i.e., L=2, 4, 6, 8, 10, and 12μm and three different values, i.e., dsi =100, 200 and 300nm, respectively. The results indicate that the greatest photo-to-dark-current contrast ratio is achieved with L=10μm and dsi=200 nm at VGK=0.6V.

Keywords: Photo-to-dark-current contrast ratio, Photo-current, Dark-current, Process parameter

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Authors: Abdussamad Ismail, Dong-Sheng Jeng

Abstract:

A self-evolution algorithm for optimizing neural networks using a combination of PSO and JPSO is proposed. The algorithm optimizes both the network topology and parameters simultaneously with the aim of achieving desired accuracy with less complicated networks. The performance of the proposed approach is compared with conventional back-propagation networks using several synthetic functions, with better results in the case of the former. The proposed algorithm is also implemented on slope stability problem to estimate the critical factor of safety. Based on the results obtained, the proposed self evolving network produced a better estimate of critical safety factor in comparison to conventional BPN network.

Keywords: Neural networks, Topology evolution, Particle swarm optimization.

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Authors: Aqeel S. Jaber, Abu Zaharin Ahmad, Ahmed N. Abdalla

Abstract:

The artificial intelligent controller in power system plays as most important rule for many applications such as system operation and its control specially Load Frequency Controller (LFC). The main objective of LFC is to keep the frequency and tie-line power close to their decidable bounds in case of disturbance. In this paper, parallel fuzzy PI adaptive with conventional PD technique for Load Frequency Control system was proposed. PSO optimization method used to optimize both of scale fuzzy PI and tuning of PD. Two equal interconnected power system areas were used as a test system. Simulation results show the effectiveness of the proposed controller compared with different PID and classical fuzzy PI controllers in terms of speed response and damping frequency.

Keywords: Load frequency control, PSO, fuzzy control.

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Authors: Mohamed Amine Ben Abdallah, Imed Khemili, Nizar Aifaoui

Abstract:

This work denotes an insight into dynamic synthesis of multibody systems. A set of mechanism parameters design variable are synthetized based on a desired mechanism response, such as, velocity, acceleration and bodies deformations. Moreover, knowing the work space, for a robot, and mechanism response allow defining optimal parameters mechanism handling with the desired target response. To this end, evolutionary genetic algorithm has been deployed. A demonstrative example for imperfect mechanism has been treated, mainly, a slider crank mechanism with a flexible connecting rod. The transversal deflection of the connecting rod has been chosen as response to identify the mechanism design parameters.

Keywords: Dynamic response, flexible bodies, optimization, evolutionary genetic algorithm.

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Authors: Paola Gattinoni, Laura Scesi

Abstract:

According to the European laws, there is the possibility of reusing the washing wastes for the environmental requalification of quarry lakes. The paper deals with the hydrogeological aspects involved in this possibility, as the introduction of finest wastes in the quarry lakes can generate alterations of the hydrogeological setting of the area, and problems for the future accessibility of the zone. To evaluate the hydrogeological compatibility of the washing wastes reuse in quarry lakes a groundwater numerical model was carried out, pointing out both the hydrogeological feasibility of this intervention and some guide lines for its optimization, in terms of inflow point with regard the groundwater flow direction and loss of volume in the quarry lake.

Keywords: Groundwater numerical modeling, hydrogeologicalalteration, quarry lake, silty-clay wastes.

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Authors: Sarah Odofin, Zhiwei Gao, Sun Kai

Abstract:

Operations, maintenance and reliability of wind turbines have received much attention over the years due to the rapid expansion of wind farms. This paper explores early fault diagnosis technique for a 5MW wind turbine system subjected to multiple faults, where genetic optimization algorithm is employed to make the residual sensitive to the faults, but robust against disturbances. The proposed technique has a potential to reduce the downtime mostly caused by the breakdown of components and exploit the productivity consistency by providing timely fault alarms. Simulation results show the effectiveness of the robust fault detection methods used under Matlab/Simulink/Gatool environment.

Keywords: Disturbance robustness, fault monitoring and detection, genetic algorithm and observer technique.

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Authors: Imran Usman, Asifullah Khan, Rafiullah Chamlawi, Abdul Majid

Abstract:

Information hiding for authenticating and verifying the content integrity of the multimedia has been exploited extensively in the last decade. We propose the idea of using genetic algorithm and non-deterministic dependence by involving the un-watermarkable coefficients for digital image authentication. Genetic algorithm is used to intelligently select coefficients for watermarking in a DCT based image authentication scheme, which implicitly watermark all the un-watermarkable coefficients also, in order to thwart different attacks. Experimental results show that such intelligent selection results in improvement of imperceptibility of the watermarked image, and implicit watermarking of all the coefficients improves security against attacks such as cover-up, vector quantization and transplantation.

Keywords: Digital watermarking, fragile watermarking, geneticalgorithm, Image authentication.

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Authors: Ning Gong, Michael Korostelev, Qiangguo Ren, Li Bai, Saroj Biswas, Frank Ferrese

Abstract:

This paper investigates the joint effect of the interconnected (n,k)-star network topology and Multi-Agent automated control on restoration and reconfiguration of power systems. With the increasing trend in development in Multi-Agent control technologies applied to power system reconfiguration in presence of faulty components or nodes. Fault tolerance is becoming an important challenge in the design processes of the distributed power system topology. Since the reconfiguration of a power system is performed by agent communication, the (n,k)-star interconnected network topology is studied and modeled in this paper to optimize the process of power reconfiguration. In this paper, we discuss the recently proposed (n,k)-star topology and examine its properties and advantages as compared to the traditional multi-bus power topologies. We design and simulate the topology model for distributed power system test cases. A related lemma based on the fault tolerance and conditional diagnosability properties is presented and proved both theoretically and practically. The conclusion is reached that (n,k)-star topology model has measurable advantages compared to standard bus power systems while exhibiting fault tolerance properties in power restoration, as well as showing efficiency when applied to power system route discovery.

Keywords: (n, k)-star Topology, Fault Tolerance, Conditional Diagnosability, Multi-Agent System, Automated Power System.

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture.

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Authors: Robert Koch, Mario Golling, Gabi Dreo

Abstract:

During the last couple of years, the degree of dependence on IT systems has reached a dimension nobody imagined to be possible 10 years ago. The increased usage of mobile devices (e.g., smart phones), wireless sensor networks and embedded devices (Internet of Things) are only some examples of the dependency of modern societies on cyber space. At the same time, the complexity of IT applications, e.g., because of the increasing use of cloud computing, is rising continuously. Along with this, the threats to IT security have increased both quantitatively and qualitatively, as recent examples like STUXNET or the supposed cyber attack on Illinois water system are proofing impressively. Once isolated control systems are nowadays often publicly available - a fact that has never been intended by the developers. Threats to IT systems don’t care about areas of responsibility. Especially with regard to Cyber Warfare, IT threats are no longer limited to company or industry boundaries, administrative jurisdictions or state boundaries. One of the important countermeasures is increased cooperation among the participants especially in the field of Cyber Defence. Besides political and legal challenges, there are technical ones as well. A better, at least partially automated exchange of information is essential to (i) enable sophisticated situational awareness and to (ii) counter the attacker in a coordinated way. Therefore, this publication performs an evaluation of state of the art Intrusion Detection Message Exchange protocols in order to guarantee a secure information exchange between different entities.

Keywords: Cyber Defence, Cyber Warfare, Intrusion Detection Information Exchange, Early Warning Systems, Joint Intrusion Detection, Cyber Conflict

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Authors: Liang Zhao, Jili Zhang, Chongquan Zhong

Abstract:

Energy consumption data, in particular those involving public buildings, are impacted by many factors: the building structure, climate/environmental parameters, construction, system operating condition, and user behavior patterns. Traditional methods for data analysis are insufficient. This paper delves into the data mining technology to determine its application in the analysis of building energy consumption data including energy consumption prediction, fault diagnosis, and optimal operation. Recent literature are reviewed and summarized, the problems faced by data mining technology in the area of energy consumption data analysis are enumerated, and research points for future studies are given.

Keywords: Data mining, data analysis, prediction, optimization, building operational performance.

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Authors: Wanyu Mao, Qiwen Sun, Weiyong Ying, Dingye Fang

Abstract:

The influence of copper promoters and reaction conditions on the formation of alcohols byproducts of a common Fischer-Tropsch synthesis used iron-based catalysts were investigated. A good compromise of 28%Cu/FeKLaSiO2 can lead to the optimization of an improved Fischer-Tropsch catalyst. The product distribution shifts towards hydrocarbons with increasing the reaction temperature, while pressure promotes the formation of alcohols. It was found that the production of either alcohols or hydrocarbons followed A-S-F distributions, and their α parameters were essentially different which indicated a competition in the growing chain between the two species. TPD after acetaldehyde adsorption gave strong evidence of the insertion of a C1 oxygen-containing species into an alkyl chain.

Keywords: Fischer-Tropsch synthesis, Fe-Cu catalyst, alcohols byproducts, reaction pathways

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Wartika, Kridanto Surendro, Husni Sastramiharja, Iping Supriana S.

Abstract:

The condition of the market is currently very dynamic, demanding organizations which is use system information to support the achievement of objectives should be necessarily improve the ability of information systems in accordance with the changes. Improved information systems capabilities need to align with the resource capabilities in internal environment of the organization, and vice versa. Alignment model between information systems and environment organizational in this capability perspective is expected can assist management in making the strategy for enhance the capability of information systems in accordance with resources internally within the organization, efficiency in the process of development, and optimization of contributions information systems in achieving organizational goals.

Keywords: Capability, alignment, information system, environmental organizations.

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Authors: Gishantha Thantulage, Tatiana Kalganova, Manissa Wilson

Abstract:

Ant Colony Algorithms have been applied to difficult combinatorial optimization problems such as the travelling salesman problem and the quadratic assignment problem. In this paper gridbased and random-based ant colony algorithms are proposed for automatic 3D hose routing and their pros and cons are discussed. The algorithm uses the tessellated format for the obstacles and the generated hoses in order to detect collisions. The representation of obstacles and hoses in the tessellated format greatly helps the algorithm towards handling free-form objects and speeds up computation. The performance of algorithm has been tested on a number of 3D models.

Keywords: Ant colony algorithm, Automatic hose routing, tessellated format, RAPID.

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Authors: Sana Bouzaida, Anis Sakly, Faouzi M'Sahli

Abstract:

In this paper, a TSK-type Neuro-fuzzy Inference System that combines the features of fuzzy sets and neural networks has been applied for the identification of MIMO systems. The procedure of adapting parameters in TSK model employs a Shuffled Frog Leaping Algorithm (SFLA) which is inspired from the memetic evolution of a group of frogs when seeking for food. To demonstrate the accuracy and effectiveness of the proposed controller, two nonlinear systems have been considered as the MIMO plant, and results have been compared with other learning methods based on Particle Swarm Optimization algorithm (PSO) and Genetic Algorithm (GA).

Keywords: Identification, Shuffled frog Leaping Algorithm (SFLA), TSK-type neuro-fuzzy model.

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Authors: E. Kaygan, A. Gatto

Abstract:

A numerical study of a design concept for actively controlling wing twist is described in this paper. The concept consists of morphing elements which were designed to provide a rigid and seamless skin while maintaining structural rigidity. The wing structure is first modeled in CATIA V5 then imported into ANSYS for structural analysis. Athena Vortex Lattice method (AVL) is used to estimate aerodynamic response as well as aerodynamic loads of morphing wings, afterwards a structural optimization performed via ANSYS Static. Overall, the results presented in this paper show that the concept provides efficient wing twist while preserving an aerodynamically smooth and compliant surface. Sufficient structural rigidity in bending is also obtained. This concept is suggested as a possible alternative for morphing skin applications. 

Keywords: Aircraft, morphing, skin, twist.

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Authors: Xiangtuo Chen, Paul-Henry Cournéde

Abstract:

Crop yield prediction is a paramount issue in agriculture. The main idea of this paper is to find out efficient way to predict the yield of corn based meteorological records. The prediction models used in this paper can be classified into model-driven approaches and data-driven approaches, according to the different modeling methodologies. The model-driven approaches are based on crop mechanistic modeling. They describe crop growth in interaction with their environment as dynamical systems. But the calibration process of the dynamic system comes up with much difficulty, because it turns out to be a multidimensional non-convex optimization problem. An original contribution of this paper is to propose a statistical methodology, Multi-Scenarios Parameters Estimation (MSPE), for the parametrization of potentially complex mechanistic models from a new type of datasets (climatic data, final yield in many situations). It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction is free of the complex biophysical process. But it has some strict requirements about the dataset. A second contribution of the paper is the comparison of these model-driven methods with classical data-driven methods. For this purpose, we consider two classes of regression methods, methods derived from linear regression (Ridge and Lasso Regression, Principal Components Regression or Partial Least Squares Regression) and machine learning methods (Random Forest, k-Nearest Neighbor, Artificial Neural Network and SVM regression). The dataset consists of 720 records of corn yield at county scale provided by the United States Department of Agriculture (USDA) and the associated climatic data. A 5-folds cross-validation process and two accuracy metrics: root mean square error of prediction(RMSEP), mean absolute error of prediction(MAEP) were used to evaluate the crop prediction capacity. The results show that among the data-driven approaches, Random Forest is the most robust and generally achieves the best prediction error (MAEP 4.27%). It also outperforms our model-driven approach (MAEP 6.11%). However, the method to calibrate the mechanistic model from dataset easy to access offers several side-perspectives. The mechanistic model can potentially help to underline the stresses suffered by the crop or to identify the biological parameters of interest for breeding purposes. For this reason, an interesting perspective is to combine these two types of approaches.

Keywords: Crop yield prediction, crop model, sensitivity analysis, paramater estimation, particle swarm optimization, random forest.

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Authors: M. Khelil, M. Boudraa, A. Kechida, R. Drai

Abstract:

Analyses carried out on examples of detected defects echoes showed clearly that one can describe these detected forms according to a whole of characteristic parameters in order to be able to make discrimination between a planar defect and a volumic defect. This work answers to a problem of ultrasonics NDT like Identification of the defects. The problems as well as the objective of this realized work, are divided in three parts: Extractions of the parameters of wavelets from the ultrasonic echo of the detected defect - the second part is devoted to principal components analysis (PCA) for optimization of the attributes vector. And finally to establish the algorithm of classification (SVM, Support Vector Machine) which allows discrimination between a plane defect and a volumic defect. We have completed this work by a conclusion where we draw up a summary of the completed works, as well as the robustness of the various algorithms proposed in this study.

Keywords: NDT, PCA, SVM, ultrasonics, wavelet

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Authors: Marwan Abukhaled, Ibrahim Sadek

Abstract:

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.

Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach

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