Control Theory Commons^™

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Mechanika Płynów Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek

HMC Senior Theses

The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.

Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, Anh V. Tran

Electronic Theses and Dissertations

The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are …

Comments On The Paper “An Alternative Combination Rule For Evidential Reasoning” By Sebbak Et Al., Published In Fusion 2014 Conference, Salamanca, Spain, July 2014, Florentin Smarandache, Jean Dezert, Arnaud Martin

Branch Mathematics and Statistics Faculty and Staff Publications

In this note we want to show that the PCR6 fusion rule works and redistributes the conflicting mass properly, contrarily to the authors’ assertion that “the focal element {v3} absorbs almost all of the conflicting mass (the majority).” We also question the validity of the new CREC rule of combination presented by the authors.

The Underlying Physiology Of Arterial Pulse Wave Morphology In Spatial Domain, Nzerem F. Egenti, Alozie H. Nkechi

Applications and Applied Mathematics: An International Journal (AAM)

Cardio-vascular events are among the world’s leading causes of morbidity and mortality. Most postulates suppose that culinary delights can be implicated in incidences of cardio-vascular diseases. This school of thought holds well in many respects. Much as the truistic value of the said school is acknowledged, we conceived of physiological disposition as an endogenous dominant factor in the events being considered, whereas culinary measures constitute an exogenous contributory factor. In this work we aimed at studying the effects of distance (stature) on pulse waveforms. Certain elements of our study showed that pulse wavelength was dominant in prescribing cardio-vascular physiology.

Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type …

Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The main control goal in fed-batch fermentation is to maximize yield of target product and reduce operation costs. In this paper, we propose a controlled nonlinear time-delay system, in which the flow rate of glycerol is taken as the control function and the terminal time of the fermentation as the optimization variable, to model the 1,3-propanediol (1,3-PD) production in fed-batch process. Taking the mass of 1,3-PD per unit time as the performance index, we formulate a constrained optimal control model with free terminal time to optimize the production process. Using a time-scale transformation, the optimal control problem is equivalently transcribed …

An Exponential Matrix Method For Numerical Solutions Of Hantavirus Infection Model, Şuayip Yüzbaşi, Mehmet Sezer

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new matrix method based on exponential polynomials and collocation points is proposed to obtain approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential equations. The method converts the model problem into a system of nonlinear algebraic equations by means of the matrix operations and the collocation points. The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all numerical computations have been made by using a computer program written in Maple.

Predator Prey Models In Competitive Corporations, Rachel Von Arb

Honors Program Projects

Predator prey models have been used for years to model animal populations. In recent years they have begun to be applied to economic situations. However, the stock market has remained largely untouched. We examine whether the success of competitive corporations such as Target and Walmart, as measured by the indicators of price per share, market share, and volume, can be modeled by various predator prey models. We consider the basic Lotka-Volterra model and the two-predator, one-prey model, as well as a ratio-dependent model. We discuss the use of numerical techniques and regression analysis as tools to estimate model parameters. For …

A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng

Xiao-Jun Yang

Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.

Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski

Wojciech Budzianowski

This article provides an analysis of processes for separation CO2 by using carbonic anhydrase enzyme with particular emphasis on reactive-membrane solutions. Three available processes are characterised. Main challenges and prospects are given. It is found that in view of numerous challenges practical applications of these processes will be difficult in near future. Further research is therefore needed for improving existing processes through finding methods for eliminating their main drawbacks such as short lifetime of carbonic anhydrase or low resistance of reactive membrane systems to impurities contained in flue gases from power plants.

Stochastic Optimal Harvesting Applied To Fisheries, Spencer Dechenne

Summer Research

We investigated alternative regularization schemes within a discrete time stochastic fishery model using stochastic dynamic programs.

Determination Of Kinetic Parameters From The Thermogravimetric Data Set Of Biomass Samples, Karol Postawa, Wojciech M. Budzianowski

Wojciech Budzianowski

This article describes methods of the determination of kinetic parameters from the thermogravimetric data set of biomass samples. It presents the methodology of the research, description of the needed equipment, and the method of analysis of thermogravimetric data. It describes both methodology of obtaining quantitative data such as kinetic parameters as well as of obtaining qualitative data like the composition of biomass. The study is focused mainly on plant biomass because it is easy in harvesting and preparation. Methodology is shown on the sample containing corn stover which is subsequently pyrolysed. The investigated sample show the kinetic of first order …

Modelling And Parameter Identification For A Nonlinear Time-Delay System In Microbial Batch Fermentation, Chongyang Liu

Chongyang Liu

Mathematical modelling and parameter identification of a microbial batch fermentation process is considered in this paper. In view of the existence of time delays, a nonlinear time-delay system is firstly proposed to formulate the fermentation process. Some important properties are also discussed. Taking the errors between the computational values and the experimental data as the cost function, a parameter identification model subject to continuous state constraints and parameter constraints is then presented. To seek the optimal time delay and the optimal kinetic parameters, an improved differential evolution algorithm in conjunction with the constraint transcription technique is developed. Finally, numerical results …

Creating The Park Cool Island In An Inner-City Neighborhood: Heat Mitigation Strategy For Phoenix, Az, Juan Declet-Barreto, Anthony J. Brazel, Chris A. Martin, Winston T. L. Chow, Sharon L. Harlan

Research Collection School of Social Sciences

We conducted microclimate simulations in ENVI-Met 3.1 to evaluate the impact of vegetation in lowering temperatures during an extreme heat event in an urban core neighborhood park in Phoenix, Arizona. We predicted air and surface temperatures under two different vegetation regimes: existing conditions representative of Phoenix urban core neighborhoods, and a proposed scenario informed by principles of landscape design and architecture and Urban Heat Island mitigation strategies. We found significant potential air and surface temperature reductions between representative and proposed vegetation scenarios: 1) a Park Cool Island effect that extended to non-vegetated surfaces; 2) a net cooling of air underneath …

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Preoperative Planning Of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Hamidreza Azimian

Electronic Thesis and Dissertation Repository

In this thesis, a computational framework for patient-specific preoperative planning of Robotics-Assisted Minimally Invasive Cardiac Surgery (RAMICS) is developed. It is expected that preoperative planning of RAMICS will improve the rate of success by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient's thorax, port locations and robot orientations (with respect to the patient's body coordinate frame) are determined to optimize characteristics such as dexterity, reachability, tool approach angles and maneuverability. In this thesis, two approaches for preoperative planning of RAMICS are proposed that …

Latin Hypercube Sampling And Partial Rank Correlation Coefficient Analysis Applied To An Optimal Control Problem, Boloye Gomero

Masters Theses

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis.

In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness …