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15
Theory and implementation of numerical methods based on RungeKutta integration for solving optimal control problems
, 1996
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A Boundary Value Problem Approach to the Optimization of Chemical Processes Described by DAE Models
, 1997
"... An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a ..."
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An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a simultaneous solution strategy) is based on a piecewise parametrization of the control functions and a multiple shooting discretization of the DAEs, combined with a specifically tailored SQP technique. The inherent problem structure is exploited on various levels in order to obtain an efficient overall method. In addition, the formulation lends itself well to parallel computation. Unlike other simultaneous strategies based on collocation, direct use is made of existing advanced, fully adaptive DAE solvers. An implementation of this strategy is provided by the recently developed modular optimal control package MUSCODII. Apart from a difficult DAE test problem with control and path constrain...
Analyse und Restrukturierung eines Verfahrens zur direkten Lösung von OptimalSteuerungsproblemen (The Theory of MUSCOD in a Nutshell)
, 1995
"... MUSCOD (MU ltiple Shooting COde for Direct Optimal Control) is the implementation of an algorithm for the direct solution of optimal control problems. The method is based on multiple shooting combined with a sequential quadratic programming (SQP) technique; its original version was developed in the ..."
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MUSCOD (MU ltiple Shooting COde for Direct Optimal Control) is the implementation of an algorithm for the direct solution of optimal control problems. The method is based on multiple shooting combined with a sequential quadratic programming (SQP) technique; its original version was developed in the early 1980s by Plitt under the supervision of Bock [Plitt81, Bock84]. The following report is intended to describe the basic aspects of the underlying theory in a concise but readable form. Such a description is not yet available: the paper by Bock and Plitt [Bock84] gives a good overview of the method, but it leaves out too many important details to be a complete reference, while the diploma thesis by Plitt [Plitt81], on the other hand, presents a fairly complete description, but is rather difficult to read. Throughout the present document, emphasis is given to a clear presentation of the concepts upon which MUSCOD is based. An effort has been made to properly reflect the structure of the a...
Dynamic Optimization Of Bioprocesses: Deterministic And Stochastic Strategies
, 1998
"... The general problem of dynamic optimization of bioprocesses with unspecified final time is considered. Several solution strategies, both deterministic and stochastic, are compared based on their results for three bioprocess case studies. A hybrid (stochasticdeterministic) method is also presented a ..."
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The general problem of dynamic optimization of bioprocesses with unspecified final time is considered. Several solution strategies, both deterministic and stochastic, are compared based on their results for three bioprocess case studies. A hybrid (stochasticdeterministic) method is also presented and evaluated, showing significant advantages in terms of robustness and computational effort. INTRODUCTION In recent years, many efforts have been devoted to the optimization and control of bioprocesses. An example of a problem that has received major attention is the dynamic optimization (open loop optimal control) of fedbatch bioreactors (e.g. van Impe, 1996; Roubos et al, 1997; Banga et al., 1997; Tholudur and Ramirez, 1997). Most bioprocesses have highly nonlinear dynamics, and constraints are also frequently present on both the state and the control variables. Thus, efficient and robust dynamic optimization methods are needed in order to successfully obtain their optimal operating po...
Optimization Strategies for Dynamic Systems
 In C. Floudas, P. Pardalos (Eds), Encyclopedia of Optimization
, 1999
"... Introduction and Problem Statement Interest in dynamic simulation and optimization of chemical processes has increased significantly during the last two decades. Common problems include control and scheduling of batch processes; startup, upset, shutdown and transient analysis; safety studies and th ..."
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Introduction and Problem Statement Interest in dynamic simulation and optimization of chemical processes has increased significantly during the last two decades. Common problems include control and scheduling of batch processes; startup, upset, shutdown and transient analysis; safety studies and the evaluation of control schemes. Chemical processes are modeled dynamically using differentialalgebraic equations (DAEs). The DAE formulation consists of differential equations that describe the dynamic behavior of the system, such as mass and energy balances, and algebraic equations that ensure physical and thermodynamic relations. The general dynamic optimization problem can be stated as follows: min z(t);y(t);u(t);t f ;p '(z(t f ); y(t f ); u(t<F8
Direct Trajectory Optimization Using a Variable LowOrder Adaptive Pseudospectral Method
 AIAA Journal of Spacecraft and Rockets
"... A variableorder adaptive pseudospectral method is presented for solving optimal control problems. The method developed in this paper adjusts both the mesh spacing and the degree of the polynomial on each mesh interval until a specified error tolerance is satisfied. In regions of relatively high cur ..."
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A variableorder adaptive pseudospectral method is presented for solving optimal control problems. The method developed in this paper adjusts both the mesh spacing and the degree of the polynomial on each mesh interval until a specified error tolerance is satisfied. In regions of relatively high curvature, convergence is achieved by refining the mesh, while in regions of relatively low curvature, convergence is achieved by increasing the degree of the polynomial. An efficient iterative method is then described for accurately solving a general nonlinear optimal control problem. Using four examples, the adaptive pseudospectral method described in this paper is shown to be more efficient than either a global pseudospectral method or a fixedorder method. Nomenclature C = path constraint function D = N N 1 Radau pseudospectral differentiation matrix E = maximum absolute solution error Fd = magnitude of drag force, N Fg = magnitude of gravity force, N Fl = magnitude of lift force, N
Optimization Framework for the Synthesis of Chemical Reactor Networks
, 1998
"... The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks ..."
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The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...
State of the Art of Research in Flexibility, Operability & Dynamics
, 1998
"... this paper and need to be defined. Flexibility commonly refers to the range of operating conditions, normally steady state conditions, which a particular process design can achieve. Switchability refers to the ability of a plant to move from alternative steady state conditions. Controllability refer ..."
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this paper and need to be defined. Flexibility commonly refers to the range of operating conditions, normally steady state conditions, which a particular process design can achieve. Switchability refers to the ability of a plant to move from alternative steady state conditions. Controllability refers to the ability of a particular design, usually including TWG3/D Bogle/R&D SoA Review/Rev P/19980112 3 the control system, to maintain safe and stable operating conditions following disturbances.
IN CHEMICAL ENGINEERING
, 2006
"... I am deeply grateful to my research advisor, Dr. Karlene A. Hoo, for her guidance and support during the four years that I was her graduate student. She has shown extreme patience in helping me understand the concepts of process control and optimization. I am also thankful to her for due diligence ..."
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I am deeply grateful to my research advisor, Dr. Karlene A. Hoo, for her guidance and support during the four years that I was her graduate student. She has shown extreme patience in helping me understand the concepts of process control and optimization. I am also thankful to her for due diligence in proofreading all of my manuscripts and this dissertation. Her financial support also is appreciated for my studies and travel to the national meeting of the American Institute of Chemical Engineering conference and technical workshops. This work would not have been possible without my parents and their constant love and support. This work is dedicated to them. I would like to thank Dr. Uzi Mann for being on my committee and providing me with the project that ultimately became central to my dissertation. I take away the need to always define the problem. Thanks also go to Dr. Gary Gladysz, for providing me with a rewarding internship at Los Alamos National Laboratory and for his service on my committee; and to Dr. Naz Karim for agreeing to serve on my committee. My academic career here has been enriched by many things including the industrial sponsors of the TTU Process Control and Optimization Consortium; and the faculty, helpful staff, and graduate students within our research group
A Novel Approach to Dynamic Optimization of ODE and DAE Systems as HighIndex Problems
, 1995
"... Solution of many problems in plant operations requires determination of optimal control profiles subject to state constraints for systems modeled by ordinary differential equations (ODEs) or differentialalgebraic equations (DAEs). For example, optimal temperature and/or feed rate profiles are im ..."
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Solution of many problems in plant operations requires determination of optimal control profiles subject to state constraints for systems modeled by ordinary differential equations (ODEs) or differentialalgebraic equations (DAEs). For example, optimal temperature and/or feed rate profiles are important for the operation of many batch reactions. Similar observations apply to reflux policies for batch distillation, and feedstock changeover in oil refineries. Currently there are two different classes of methods for determining optimal control profiles for DAEs. Control parameterization techniques rely on the discretization of the control variables to reduce the optimal control problem to an NLP. These methods require repeated integration of the DAEs and some variational equations, which effectively discretizes the state variables within the numerical integrator. Path constraints are typically handled by the master NLP solver, and can force the NLP solver to call for a large nu...