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Non-intrusive Time-POD for Optimal Control of a Fixed-Bed Reactor for CO 2 Methanation

IFAC-PapersOnLine 2021年第3期54卷 122-127页

作者： Jens Bremer Jan Heiland Peter Benner Kai Sundmacher Max Planck Institute Magdeburg Dpt. Process Systems Engineering Sandtorstraße 2 39106 Magdeburg Germany and Otto von Guericke University Magdeburg Chair for Process Systems Engineering Universitätsplatz 2 39106 Magdeburg (Sundmacher) Max Planck Institute Magdeburg Dpt. Computational Methods in Systems and Control Theory and Otto von Guericke University Magdeburg Fakultät für Mathematik

The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box optimization algorithm to a parameterized control scheme. The success then depends on the quality of the parametrization that should be low-dimensional though rich enough to express the salient features. This work proposes using solution snapshots to extract dominant modes of the temporal dynamics of a process and use them for low-dimensional parametrizations of control functions. The approach is called proper orthogonal decomposition in time (time-POD). We provide theoretical reasoning and illustrate the performance for the optimal control of a methanation reactor.

关键词： Optimal control Model order reduction Proper orthogonal decomposition Fixed-bed reactor Carbon dioxide methanation nonlinear programming Black-box model

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nonlinear OPTIMAL CONTROL OF A DEEP BOREHOLE TRAJECTORY DESIGN 39

NONLINEAR OPTIMAL CONTROL OF A DEEP BOREHOLE TRAJECTORY DESI...

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ASME 39th International Conference on Ocean, Offshore and Arctic Engineering (OMAE)

作者： Gulyayev, Valery Glazunov, Sergii Andrusenko, Olena Natl Transport Univ Kiev Ukraine

ISBN: (纸本)9780791884317

In modern oil/gas producing industry, vertical, 2D and 3D directed, and multilateral (branched) boreholes are drilled. Their trajectories are designed depending on the petroleum deposit depth and structure, properties of mining rocks, their hardness, heterogeneity, fracturing anisotropy, permeability, and so on. Therefore, the borehole cost and its productivity are determined by the length, smoothness, and configuration of its trajectory. To enhance efficiency of a borehole and to reduce cost of its drivage, to enlarge rate and volume of the reservoir depletion, it is proposed to use methods of optimal control for the best tracking of its trajectory. Through application of the differential geometry correlations, the mathematic model of the borehole outline in the form of nonlinear ordinary differential equations system is elaborated. Different objective functions, representing total integral curvature of the borehole axis line, its length, and cost of its drivage, are selected;additional constraints, separating allowed and forbidden zones of passing, are chosen. The functions of the trajectory curvature and torsion are used as controlling variables. The continuous correlations of the model are discretized and, further, the techniques of nonlinear programming and optimal control are employed. On the basis of the method of objective function gradient (antigradient) projection on the linearized constraint planes, the step-by-step algorithm of approaching to the optimal trajectory is elaborated. To correct the spoilt constraints, at every step of calculations, the Newton method is used. The elaborated approach is applied to optimization of deep curvilinear borehole outlines. The results of numerical analysis are discussed. It is shown that smoothing the hole trajectory permits also to diminish the contact and frictional interaction between the drill string and bore-hole wall and, by this, to decrease the resistance forces acting on the string during tripping in/out oper

关键词： String Permeability Drill strings Numerical analysis Trajectories (Physics) nonlinear programming Fracture (Process) Reservoirs Differential equations Algorithms Geometry Design Optimal control Wear Mining Probability Rocks Optimization Newton's method Torsion Petroleum Anisotropy

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Supporting Education in Algorithms of Computational Mathematics by Dynamic Visualizations Using Computer Algebra System 20th

Supporting Education in Algorithms of Computational Mathemat...

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20th Annual International Conference on Computational Science (ICCS)

作者： Wojas, Wlodzimierz Krupa, Jan Warsaw Univ Life Sci SGGW Dept Appl Math Ul Nowoursynowska 159 PL-02776 Warsaw Poland

ISBN: (纸本)9783030504366;9783030504359

Computer algebra systems (CAS) are often used programs in universities to support calculations and visualization in teaching mathematical subjects. In this paper we present some examples of dynamic visualizations which we prepared for students of Warsaw University of Life Sciences using Mathematica. Visualizations for simplex algorithm and Karush-Kuhn-Tucker algorithm are presented. We also describe a didactic experiment for students of the Production Engineering Faculty of Warsaw University of Life Sciences using dynamic visualization of the network flow problem.

关键词： Computational mathematics Symbolic calculations Mathematical didactics Linear programming nonlinear programming Network flows CAS

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Comparison of Derivative Estimation Methods in Solving Optimal Control Problems Using Direct Collocation

Comparison of Derivative Estimation Methods in Solving Optim...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Agamawi, Yunus M. Rao, Anil, V Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32611 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular, the Taylor series-based finite-difference, bicomplex-step, and hyper-dual derivative estimation methods are evaluated and compared alongside a well known automatic differentiation method. The performance of each derivative estimation method is assessed based on the number of iterations, the computation time per iteration, and the total computation time required to solve the nonlinear programming problem. The efficiency of each of the four derivative estimation methods is compared by solving three benchmark optimal control problems. It is found that while central finite-differencing is typically more efficient per iteration than either the hyper-dual or bicomplex-step, the latter two methods have significantly lower overall computation times due to the fact that fewer iterations are required by the nonlinear programming problem when compared with central finite-differencing. Furthermore, while the bicomplex-step and hyper-dual methods are similar in performance, the hyper-dual method is significantly easier to implement. Moreover, the automatic differentiation method is found to be substantially less computationally efficient than any of the three Taylor series-based methods. The results of this study show that the hyper-dual method offers several benefits over the other three methods both in terms of computational efficiency and ease of implementation.

关键词： Time Optimal Control nonlinear programming Gaussian Quadrature Taylor Series Finite Difference Approximation Computer Programs Computing Supersonic Aircraft Free Flying Robots Space Stations

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The multi-objective supplier selection problem with fuzzy parameters and solving the order allocation problem with coverage

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JOURNAL OF MODELLING IN MANAGEMENT 2020年第3期15卷 705-725页

作者： Khalilzadeh, Mohammad Karami, Arya Hajikhani, Alborz Pontificia Univ Catolica Peru CENTRUM Catolica Grad Business Sch Lima Peru Sharif Univ Technol Fac Ind Engn Tehran Iran Islamic Azad Univ Sci & Res Branch Dept Ind Engn Tehran Iran

Purpose This study aims to deal with supplier selection problem. The supplier selection problem has significantly become attractive to researchers and practitioners in recent years. Many real-world supply chain problems are assumed as multiple objectives combinatorial optimization problems. Design/methodology/approach In this paper, the authors propose a multi-objective model with fuzzy parameters to select suppliers and allocate orders considering multiple periods, multiple resources, multiple products and two-echelon supply chain. The objective functions consist of total purchase costs, transportation, order and on-time delivery, coverage and the weights of suppliers. Distance-based partial and general coverage of suppliers makes the number of orders of products more realistic. In this model, the weights of suppliers are determined by fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, as a multi-criteria decision analysis method, in the objective function. Also, the authors consider the parameters related to delays as triangular fuzzy numbers. Findings A small-sized numerical example is provided to clearly show the proposed model. The exact epsilon constraint method is used to solve this given multi-objective combinatorial optimization problem. Subsequently, the sensitivity analysis is conducted to testify the proposed model. The obtained results demonstrate the validity of the proposed multiple objectives mixed integer mathematical programming model and the efficiency of the solution approach. Originality/value In real-life situations, supplier selection parameters are uncertain and incomplete. Hence, the fuzzy set theory is used to tackle uncertainty. In this paper, a multi-objective supplier selection problem is formulated taking into consideration the coverage of suppliers and suppliers' weights. Integrating coverage of suppliers to select and allocate the order to them can be mentioned as the main contribution of this stu

关键词： Decision-making Optimisation nonlinear programming Multi-criteria programming Fuzzy set Epsilon-constraint method

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A Proximal Method for the Numerical Solution of Singular Optimal Control Problems Using a Modified Radau Collocation Method

A Proximal Method for the Numerical Solution of Singular Opt...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Pager, Elisha R. Rao, Anil, V Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32611 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

A proximal method is developed for solving optimal control problems whose solutions contain a singular arc. The method employs a regularization technique previously established in literature using a modified Legendre-Gauss-Radau (LGR) orthogonal direct collocation method. The cost functional of a singular optimal control problem is modified by the addition of an integral term and then transcribed into a nonlinear programming (NLP) problem using a modified LGR collocation scheme. This modification to the optimal control problem transcribes the original singular NLP into a nonsingular NLP that is now solved iteratively until an approximation of the original singular solution is achieved within some error tolerance. Finally, the accuracy and effectiveness of this proposed method is demonstrated on an optimal control problem with a known solution whose structure is bang-singular.

关键词： Gaussian Quadrature Legendre Clebsch Condition nonlinear programming MATLAB Computing

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Quadrupedal Robotic Walking on Sloped Terrains via Exact Decomposition into Coupled Bipedal Robots

Quadrupedal Robotic Walking on Sloped Terrains via Exact Dec...

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IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Ma, Wen-Loong Csomay-Shanklin, Noel Ames, Aaron D. CALTECH Dept Mech Engn Pasadena CA 91125 USA CALTECH Dept Control Dynam Syst Pasadena CA 91125 USA

ISBN: (纸本)9781728162126

Can we design motion primitives for complex legged systems uniformly for different terrain types without neglecting modeling details? This paper presents a method for rapidly generating quadrupedal locomotion on sloped terrains-from modeling to gait generation, to hardware demonstration. At the core of this approach is the observation that a quadrupedal robot can be exactly decomposed into coupled bipedal robots. Formally, this is represented through the framework of coupled control systems, wherein isolated subsystems interact through coupling constraints. We demonstrate this concept in the context of quadrupeds and use it to reduce the gait planning problem for uneven terrains to bipedal walking generation via hybrid zero dynamics. This reduction method allows for the formulation of a nonlinear optimization problem that leverages low-dimensional bipedal representations to generate dynamic walking gaits on slopes for the full-order quadrupedal robot dynamics. The result is the ability to rapidly generate quadrupedal walking gaits on a variety of slopes. We demonstrate these walking behaviors on the Vision 60 quadrupedal robot;in simulation, via walking on a range of sloped terrains of 13 degrees, 15 degrees, 20 degrees, 25 degrees, and, experimentally, through the successful locomotion of 13 degrees and 20 degrees similar to 25 degrees sloped outdoor grasslands.

关键词： nonlinear programming

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Simultaneous Vehicle and Trajectory Design using Convex Optimization

Simultaneous Vehicle and Trajectory Design using Convex Opti...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Lin, Beldon Carpenter, Michele de Weck, Olivier Charles Stark Draper Lab Inc Cambridge MA 02139 USA MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

Convex optimization is used to solve the simultaneous vehicle and trajectory optimization problem. The objective of this work is to develop a method that allows the influence of trajectory design to be taken into account in the conceptual design stage. The vehicle and trajectory optimization problems can be solved individually using convex optimization through the use of geometric programming and successive convexification techniques respectively. These formulations allow the problem to be solved very quickly while maintaining similar fidelity to comparable methods. Three different architectures that combine these formulations into one single optimization process are formulated, and two are implemented and evaluated for a sounding rocket design problem. The methodology proves successful in designing the sounding rocket while taking into account the optimal trajectory. The results are analyzed and discussed, and future improvements to the methodology are discussed.

关键词： nonlinear programming Trajectory Optimization Sounding Rockets Drag Coefficient Supersonic Flow Multidisciplinary Design Optimization Gauss Pseudospectral Method Thermal Protection System Aircraft Design Process Goddard Problem

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Longitudinal control of transition to powered flight for a parachute-dropped multirotor

Longitudinal control of transition to powered flight for a p...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Opazo, Tomas, I Langelaan, Jack W. Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

The problem of controlling the safe transition of a multirotor vehicle between its release from a parachute to the moment it reaches steady state flight is analyzed. The problems of optimal trajectory, controller tuning, safety and stability to initial conditions are also studied. The proposed solution involves a two step process to find a safe controller. First, an optimal control problem is defined and then transcribed, using a direct collocation method, into a nonlinear programming problem. Second, the trajectory error for a subset of initial conditions is calculated, and the worst case is defined as the overall cost. This emerging Min-Max problem is then solved using particle swarm optimization to obtain the best set of controller gains. In order to evaluate performance, a cost function based on margins between the vehicle's state and their respective maximum allowable values was defined. Monte Carlo simulations were ran over the space of possible initial conditions. The combination of optimal trajectory and particle swarm derived controller gains results in an average state cost reduction of 23% when compared to a near-hover controller derived using Ziegler-Nichols method.

关键词： Multicopter Longitudinal Control Particle Swarm Optimization Monte Carlo Simulation nonlinear programming Trajectory Optimization Collocation Method Cost Reduction Aerodynamic Torque Electronic Speed Control

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Adaptive Radau pseudo-spectral optimization for descending trajectory of a hypersonic cruise vehicle

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Aerospace Systems 2020年第4期3卷 275-286页

作者： Feng, Xinle Lv, Yali Gao, Yang Li, Yuankai Province Key Laboratory of Aircraft Swarm Intelligent Sensing and Cooperative Control University of Electronic Science and Technology of China Chengdu 611731 China

During descending flight of a hypersonic cruise vehicle (HCV), the flight environment is complicated due to the drastically changed atmosphere. It is necessary for the flight trajectory to perform accurate and fast optimization. To solve the nonlinear optimization problem, in this paper, a global adaptive Radau pseudo-spectral method, which is introduced with an hp adaptive strategy (p method to increase the number of points in time interval and h method to refine the interval) is presented. The maximum range and the shortest engagement time are considered, respectively, as performance index to optimize controlling of the attack angle. Using Lagrange interpolation polynomial approximation, the optimal control problem is transformed into a problem of nonlinear programming and solved by a sequence quadratic programming algorithm. Simulation results have shown that the presented method has high computational efficiency and desirable accuracy, with the flying constraints satisfied. It is an effective trajectory optimization method for HCVs. © 2020, Shanghai Jiao Tong University.

关键词： Adaptive Radau pseudo-spectral method Aerodynamic data fitting nonlinear programming Optimal control Trajectory optimization

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