Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, 2014 Curtin University of Technology

#### Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the ...

A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, 2014 Curtin University of Technology

#### A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system ...

Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, 2014 Shandong Institute of Business and Technology

#### Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary ...

Termodynamika Procesowa I Techniczna Lab., 2014 Wroclaw University of Technology

#### Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., 2014 Wroclaw University of Technology

#### Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., 2014 Wroclaw University of Technology

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

*Wojciech Budzianowski*

No abstract provided.

Mechanika Płynów Lab., 2014 Wroclaw University of Technology

#### Mechanika Płynów Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, 2014 Georgia Southern University

#### 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 ...

A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, 2014 Harvey Mudd College

#### 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.

Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, 2013 Dalian University of Technology

#### 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 ...

Predator Prey Models In Competitive Corporations, 2013 Olivet Nazarene University

#### 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, 2013 China University of Mining & Technology

#### 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., 2013 Wroclaw University of Technology

#### Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, 2013 Wroclaw University of Technology

#### 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, 2013 University of Puget Sound

#### 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, 2012 Wroclaw University of Technology

#### 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, 2012 Shandong Institute of Business and Technology

#### 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 ...

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, 2012 The University of Western Ontario

#### 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, 2012 The University of Western Ontario

#### 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 ...

Latin Hypercube Sampling And Partial Rank Correlation Coefficient Analysis Applied To An Optimal Control Problem, 2012 University of Tennessee, Knoxville

#### 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 ...