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RealTime Optimization and Nonlinear Model Predictive Control of Processes Governed By DifferentialAlgebraic Equations
, 2001
"... Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast offline method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performan ..."
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Cited by 28 (12 self)
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Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast offline method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briey reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of realtime optimization. Special strategies have been developed to effectively minimize the online computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical realtime problems they have proven much faster than fast offline strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice.
SQP Methods And Their Application To Numerical Optimal Control
, 1997
"... . In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown ..."
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Cited by 19 (0 self)
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. In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying generalpurpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. largescale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...
Reduced SQP Methods for LargeScale Optimal Control Problems in DAE with Application to Path Planning Problems for Satellite Mounted Robots
, 1996
"... and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ..."
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Cited by 16 (7 self)
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and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ODE : : : : : : : : : : : : : : : : : : : : 11 2.1.1 Choice of collocation points : : : : : : : : : : : : : : : : : : : : : : 14 2.1.2 The polynomial representation : : : : : : : : : : : : : : : : : : : : : 14 2.1.3 A tempting combination : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Collocation for BVP in DAE with invariants : : : : : : : : : : : : : : : : : 17 2.2.1 DAE models from mechanics : : : : : : : : : : : : : : : : : : : : : : 17 2.2.2 Collocation discretization of two point BVP in DAE : : : : : : :
Numerical Optimal Control Of Parabolic PDEs Using DASOPT
, 1997
"... . This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package ..."
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Cited by 11 (6 self)
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. This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package for largescale optimization based on sequential quadratic programming (SQP). DASOPT is intended for the computation of the optimal control of timedependent nonlinear systems of PDEs in two (and eventually three) spatial dimensions, including possible inequality constraints on the state variables. By the use of either finitedifference or finiteelement approximations to the spatial derivatives, the PDEs are converted into a large system of ODEs or DAEs. Special techniques are needed in order to solve this very large optimal control problem. The use of DASOPT is illustrated by its application to a nonlinear parabolic PDE boundary control problem in two spatial dimensions. Computational resu...
Mathematical Optimization in Robotics: Towards Automated High Speed Motion Planning
 Math. Ind
, 1997
"... ly, the set of orientation matrices SO(3) ae R 3\Theta3 is a compact 3dimensional C 1 submanifold which has no global 3parameter representation without singularities. Consider a point p fixed on a moving body. Its inertial position and velocity are p 0 (t) = r(t) + R(t)p and p 0 (t) = r(t) ..."
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Cited by 10 (8 self)
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ly, the set of orientation matrices SO(3) ae R 3\Theta3 is a compact 3dimensional C 1 submanifold which has no global 3parameter representation without singularities. Consider a point p fixed on a moving body. Its inertial position and velocity are p 0 (t) = r(t) + R(t)p and p 0 (t) = r(t) + R(t)p, respectively. The rotation part can be written Rp = ! 0 \Theta (Rp) = (R!) \Theta (Rp) = R(! \Theta p); where ! and ! 0 are the angular velocities in the body frame and inertial frame, respectively. On the other hand, we have ! \Theta p = ~ !p where ~ ! := 0 @ 0 \Gamma! 3 ! 2 ! 3 0 \Gamma! 1 \Gamma! 2 ! 1 0 1 A = \Gamma ~ ! 2 A(3) is an antisymmetric matrix; the corresponding inertial angular velocity matrix is ~ ! 0 = R~!R . (Asterisk superscripts denote transposition throughout the paper.) The above relations define a sequence of canonical linear isomorphisms between R 3 and the tangent space of SO(3) at R (the matrix velocity space), TRSO(3) = RA(3) ¸ = A(3) ¸ =...
Partially Reduced SQP Methods For LargeScale Nonlinear Optimization Problems
, 1997
"... this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations: ..."
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Cited by 5 (0 self)
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this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations:
Efficient Nonlinear Model Predictive Control
, 2001
"... The growing interest in model predictive control for nonlinear systems is motivated by the fact that today's processes need to be operated under tighter performance specifications to guarantee profitable and environmentally safe production. Nonlinear model predictive control (NMPC) does allow the di ..."
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Cited by 4 (4 self)
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The growing interest in model predictive control for nonlinear systems is motivated by the fact that today's processes need to be operated under tighter performance specifications to guarantee profitable and environmentally safe production. Nonlinear model predictive control (NMPC) does allow the direct consideration of a nonlinear process model as well as state and input constraints. Thus NMPC seems to be well suited for these kind of processes. Many theoretical issues in NMPC have been attacked and solved in recent years. Despite this progress there are a number of problems that have to be solved before NMPC can be applied in practice.
Realtime Feasibility of Nonlinear Predictive Control for Large Scale Processes  a Case Study
, 2000
"... Despite many control theoretic and numerical advances, up to now there is no realistic feasibility study of modern nonlinear model predictive control (NMPC) schemes for the realtime control of largescale processes. In this paper the application of NMPC to a nontrivial process control example, name ..."
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Cited by 4 (3 self)
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Despite many control theoretic and numerical advances, up to now there is no realistic feasibility study of modern nonlinear model predictive control (NMPC) schemes for the realtime control of largescale processes. In this paper the application of NMPC to a nontrivial process control example, namely the control of a highpurity binary distillation column, is considered. Using models of di erent complexity and different control schemes, the computational load, resulting closed loop performance and the effort needed to design the controllers is compared. It is shown that a realtime application of modern NMPC schemes is feasible with existing techniques, even for a 164 order model with a sampling time of 30 s, if a state of the art dynamic optimization algorithm and an efficient NMPC scheme are used.
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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Cited by 3 (0 self)
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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
ComputerAided Motion Planning For Satellite Mounted Robots
, 1998
"... In space based robotics, one of the most important problems is the disturbance to the satellite attitude and to the satellite microgravity environment caused by satellite mounted robot operation. This paper reports on computeraided motion planning strategies to overcome this problem. Point to point ..."
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Cited by 2 (1 self)
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In space based robotics, one of the most important problems is the disturbance to the satellite attitude and to the satellite microgravity environment caused by satellite mounted robot operation. This paper reports on computeraided motion planning strategies to overcome this problem. Point to point motion designs are generated which not only connect prescribed start and end points of the robot motion, but also simultaneously return the satellite to its original attitude. Theoretical characterizations of some of those motion designs are presented, as well as numerical results. The computation time required to produce such motion designs is 1 or 2 minutes on a workstation. Thus, it can be practical to use these motion plans in space. Introduction Satellite mounted robots can aid in the automated assembly of large structures in space and sometimes eliminate the need for extravehicular activity or "space walks", which are timeconsuming and dangerous for astronauts. Robots in space can ...