Search results for: optimal control with elliptic partial differential equation constraint

Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Piyush V. Surjagade, Jiamei Deng, Paul Doney, S. R. Shimjith, A. John Arul

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In sophisticated and complex systems such as nuclear power plants, maintaining the system's stability in the presence of uncertainties and disturbances and obtaining a fast dynamic response are the most challenging problems. Thus, to ensure the satisfactory and safe operation of nuclear power plants, this work proposes a new fast, robust optimal switching control strategy for pressurized water reactor-type nuclear power plants. The proposed control strategy guarantees a substantial degree of robustness, fast dynamic response over the entire operational envelope, and optimal performance during the nominal operation of the plant. To improve the robustness, obtain a fast dynamic response, and make the system optimal, a bank of controllers is designed. Various controllers, like a baseline proportional-integral-derivative controller, an optimal linear quadratic Gaussian controller, and a robust adaptive L1 controller, are designed to perform distinct tasks in a specific situation. At any instant of time, the most suitable controller from the bank of controllers is selected using the switching logic unit that designates the controller by monitoring the health of the nuclear power plant or transients. The proposed switching control strategy optimizes the overall performance and increases operational safety and efficiency. Simulation studies have been performed considering various uncertainties and disturbances that demonstrate the applicability and effectiveness of the proposed switching control strategy over some conventional control techniques.

Keywords: switching control, robust control, optimal control, nuclear power control

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Authors: Salihah Alghamdi, Surajit Ray

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Space-time data can be observed over irregularly shaped manifolds, which might have complex boundaries or interior gaps. Most of the existing methods do not consider the shape of the data, and as a result, it is difficult to model irregularly shaped data accommodating the complex domain. We used a method that can deal with space-time data that are distributed over non-planner shaped regions. The method is based on partial differential equations and finite element analysis. The model can be estimated using a penalized least squares approach with a regularization term that controls the over-fitting. The model is regularized using two roughness penalties, which consider the spatial and temporal regularities separately. The integrated square of the second derivative of the basis function is used as temporal penalty. While the spatial penalty consists of the integrated square of Laplace operator, which is integrated exclusively over the domain of interest that is determined using finite element technique. In this paper, we applied a spatio-temporal regression model with partial differential equations regularization (ST-PDE) approach to analyze a remote sensing data measuring the greenness of vegetation, measure by an index called enhanced vegetation index (EVI). The EVI data consist of measurements that take values between -1 and 1 reflecting the level of greenness of some region over a period of time. We applied (ST-PDE) approach to irregular shaped region of the EVI data. The approach efficiently accommodates the irregular shaped regions taking into account the complex boundaries rather than smoothing across the boundaries. Furthermore, the approach succeeds in capturing the temporal variation in the data.

Keywords: irregularly shaped domain, partial differential equations, finite element analysis, complex boundray

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Tomoaki Hashimoto

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Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

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Authors: Abdelaziz Rabhi, Mohamed Amrani, Abderrazek Ziane, Nabil Belkadi, Abdelraouf Hocini

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In this paper, a bedimensional simulation program of the electric characteristics of reverse biased lateral polysilicon PIN diode is presented. In this case we have numerically solved the system of partial differential equations formed by Poisson's equation and both continuity equations that take into account the effect of impact ionization. Therefore we will obtain the current-voltage characteristics (I-V) of the reverse-biased structure which may include the effect of breakdown.The geometrical model assumes that the polysilicon layer is composed by a succession of defined mean grain size crystallites, separated by lateral grain boundaries which are parallel to the metallurgic junction.

Keywords: breakdown, polycrystalline silicon, PIN, grain, impact ionization

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Authors: Hossein Abbasi

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The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modelling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they are designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: frequency control, HS algorithm, microgrid, PI controller, voltage control

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Authors: M. Alam, P. Seshaiyer

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The rupture predictability of intracranial aneurysm is one of the most important parameters for physicians in surgical treatment. As most of the intracranial aneurysms are asymptomatic, still the rupture potential of both symptomatic and asymptomatic lesions is relatively unknown. Moreover, an intracranial aneurysm constrained by a nerve tissue might be a common scenario for a physician to deal with during the treatment process. Here, we perform a computational modeling of nerve tissue constrained intracranial saccular aneurysm to show a protective role of constrained tissue on the aneurysm. A comparative parametric study of the model also performs taking long constraint, medium constraint, short constraint, point contact, narrow neck aneurysm, wide neck aneurysm as parameters for the analysis. Results show that contact constraint aneurysm generates less stress near the fundus compared to no constraint aneurysm, hence works as a protective wall for the aneurysm not to be ruptured.

Keywords: rupture potential, intracranial saccular aneurysm, anisotropic hyper-elastic material, finite element analysis

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Authors: Uyanga Sukhbaatar, Ahmed Lbath, Mendamar Majig

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The Orienteering Problem is the most known example to start modeling tourist trip design problem. In order to meet tourist’s interest and constraint the OP is becoming more and more complicate to solve. The Multi Constraint Team Orienteering Problem with Time Windows is the last extension of the OP which differentiates from other extensions by including more extra associated constraints. The goal of the MCTOPTW is maximizing tourist’s satisfaction score in same time not to violate any of these constraints. This paper presents a genetic algorithmic approach to tackle the MCTOPTW. The benchmark data from literature is tested by our algorithm and the performance results are compared.

Keywords: multi constraint team orienteering problem with time windows, genetic algorithm, tour planning system

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Hwan Su Jung, Ahn Jun Gil, Jong Tae Kim

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Power management techniques are necessary to save power in the microprocessor. By changing the frequency and/or operating voltage of processor, DVFS can control power consumption. In this paper, we perform a case study to find optimal power state transition for DVFS. We propose the equation to find the optimal ratio between executions of states while taking into account the deadline of processing time and the power state transition delay overhead. The experiment is performed on the Cortex-M4 processor, and average 6.5% power saving is observed when DVFS is applied under the deadline condition.

Keywords: deadline, dynamic voltage frequency scaling, power state transition

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Sayed Kifayat Shah, Tang Zhongjun, Mohammad Ahmad, Sohaib Mostafa

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This article investigates consumer’s intention to shift to 5G in the light of disruptive technology innovation. To switch from 4G (Existing) technology to 5G (Disruptive) technology requires not just economic benefits and costs but involves other values too, which aren't yet experienced in the framework of technology innovation. This study extended the valued adaptation (VAM) model by proposing the sustainability values (SVs) construct. The model was examined on data from 361 Chinese consumers using the partial least squares-based structural equation modelling (PLS-SEM) technique. The outcomes prove the significant correlation of sustainability values (SVs) which influences consumer’s switching intentions toward 5G disruptive technology. The findings of this research will be helpful to telecoms firms in developing consumer retention strategies. Some limitations and the importance of the research for scholars and managers are also discussed.

Keywords: value adaptation model (VAM), sustainability values (SVs), disruptive 5G technology, switching intentions (SI), partial least squares-based structural equation modelling (PLS-SEM)

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Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: D. M. S. Bandara, Yunqi Lei, Ye Luo

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Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.

Keywords: arnold cat map, biometric encryption, block cipher, elliptic curve cryptography, fingerprint encryption, Koblitz’s encoding

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Nader Ghareeb, Rüdiger Schmidt

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Minimizing the weight in flexible structures means reducing material and costs as well. However, these structures could become prone to vibrations. Attenuating these vibrations has become a pivotal engineering problem that shifted the focus of many research endeavors. One technique to do that is to design and implement an active control system. This system is mainly composed of a vibrating structure, a sensor to perceive the vibrations, an actuator to counteract the influence of disturbances, and finally a controller to generate the appropriate control signals. In this work, two different techniques are explored to create two different mathematical models of an active control system. The first model is a finite element model with a reduced number of nodes and it is called a super-element. The second model is in the form of state-space representation, i.e. a set of partial differential equations. The damping coefficients are calculated and incorporated into both models. The effectiveness of these models is demonstrated when the system is excited by its first natural frequency and an active control strategy is developed and implemented to attenuate the resulting vibrations. Results from both modeling techniques are presented and compared.

Keywords: damping coefficients, finite element analysis, super-element, state-space model

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: Kritika Bansal, Akwinder Kaur, Shruti Gujral

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In this paper, the approach of denoising is solved by using a new hybrid technique which associates the different denoising methods. Wavelet thresholding and anisotropic diffusion filter are the two different filters in our hybrid techniques. The Wavelet thresholding removes the noise by removing the high frequency components with lesser edge preservation, whereas an anisotropic diffusion filters is based on partial differential equation, (PDE) to remove the speckle noise. This PDE approach is used to preserve the edges and provides better smoothing. So our new method proposes a combination of these two filtering methods which performs better results in terms of peak signal to noise ratio (PSNR), coefficient of correlation (COC) and equivalent no of looks (ENL).

Keywords: denoising, anisotropic diffusion filter, multiplicative noise, speckle, wavelets

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Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

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The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: entropy generation, hybrid nano fluid, heat transfer, porous disks

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Authors: Leila Jafari, Viliam Makis, G. B. Akram Khaleghei

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In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1, which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM, has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed and illustrated by a numerical example.

Keywords: condition-based maintenance, semi-Markov decision process, multivariate Bayesian control chart, partially observable system, two-unit system

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Authors: Soltani Amir, Hu Jiaxin

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Determination of optimal parameters of a passive control system device is the primary objective of this study. Expanding upon the use of control devices in wind and earthquake hazard reduction has led to development of various control systems. The advantage of non-linearity characteristics in a passive control device and the optimal control method using LQR algorithm are explained in this study. Finally, this paper introduces a simple approach to determine optimum parameters of a nonlinear viscous damper for vibration control of structures. A MATLAB program is used to produce the dynamic motion of the structure considering the stiffness matrix of the SDOF frame and the non-linear damping effect. This study concluded that the proposed system (variable damping system) has better performance in system response control than a linear damping system. Also, according to the energy dissipation graph, the total energy loss is greater in non-linear damping system than other systems.

Keywords: passive control system, damping devices, viscous dampers, control algorithm

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Maryamosadat Ghasemi, Reza Amrollahi

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Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be able to support this plasma equilibrium geometry. In this work the prepared numerical code based on radial basis functions are presented and used to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of tokamak plasma. The radial basis functions (RBFs) which is a kind of numerical meshfree method (MFM) for solving partial differential equations (PDEs) has appeared in the last decade and is developing significantly in the last few years. This technique is applied in this study to obtain the equilibrium configuration for Alborz Tokamak. The behavior of numerical solution convergences show the validation of this calculations.

Keywords: equilibrium, grad–shafranov, radial basis functions, Alborz Tokamak

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Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

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In order to sustain the advantages of an advanced manufacturing technique, such as laser sintering, minimization of total processing cost of the parts being produced is very important. An efficient time management would usually very important in optimal cost attainment which would ultimately result in an efficient advanced manufacturing process planning and control. During Laser Scanning Process Scanning (SLS) procedures it is possible to adjust various manufacturing parameters which are used to influence the improvement of various mechanical and other properties of the products. In this study, Modelling and mathematical analysis, including sensitivity analysis, of the laser sintering process time were carried out. The results of the analyses were represented with graphs, from where conclusions were drawn. It was specifically observed that achievement of optimal total scanning time is key for economic efficiency which is required for sustainability of the process.

Keywords: modeling and analysis, optimal planning and control, laser sintering process, scanning time

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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An investigation is made for unsteady MHD thin film flow of a third grade fluid down an inclined plane with slip boundary condition. The non-linear partial differential equation governing the flow and heat transfer are evaluated numerically using computer software called Maple to obtain velocity and temperature profile. The effect of slip and other various physical parameter on both velocity and temperature profile obtained are studied through several graphs.

Keywords: non-Newtonian fluid, MHD flow, third-grade fluid, Maple, slip boundary condition, heat transfer

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Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale

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These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.

Keywords: elastic beam, moving load, response of structure, variable elastic foundation

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Authors: Sunsoo Kim, Niladri Das, Raktim Bhattacharya

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This paper addresses modeling and control of a six-degree-of-freedom unmanned aerial vehicle capable of vertical take-off and landing in the presence of wind disturbances. We design a hybrid vehicle that combines the benefits of both the fixed-wing and the rotary-wing UAVs. A non-linear model for the hybrid vehicle is rapidly built, combining rigid body dynamics, aerodynamics of wing, and dynamics of the motor and propeller. Further, we design a H₂ optimal controller to make the UAV robust to wind disturbances. We compare its results against that of proportional-integral-derivative and linear-quadratic regulator based control. Our proposed controller results in better performance in terms of root mean squared errors and time responses during two scenarios: hover and level- flight.

Keywords: hybrid UAVs, VTOL, aircraft modeling, H2 optimal control, wind disturbances

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