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Dynamic optimization using a wavelet based adaptive control vector parameterization strategy

COMPUTERS & CHEMICAL ENGINEERING 2000年第2-7期24卷 1201-1207页

作者： Binder, T Cruse, A Villar, CAC Marquardt, W Rhein Westfal TH Aachen Lehrstuhl Prozesstech D-52056 Aachen Germany Col San Pedro Dept Ingn Elect San Pedro Zacatenco Mexico

In this work we present an adaptive parameterization strategy for the so-called sequential solution approach where the optimization problem is approximated by a nonlinear program (NLP) by parameterization of the control variables only. The proposed method is embedded into a solution methodology where a hierarchy of successively refined finite dimensional optimization problems are solved. Information on the solution of the coarser approximation is used to construct a fully adaptive, problem dependent parameterization. The adaptation is built on a multiscale setting involving wavelets. We demonstrate examplarily that the adaptive parameterization is more efficient and robust compared with a uniform parameterization of comparable accuracy. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： dynamic optimization large scale systems adaptive mesh refinement control vector parameterization single shooting wavelets

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control vector parameterization method with time nodes parameters

Control vector parameterization method with time nodes param...

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6th World Congress on Intelligent control and Automation

作者： Zhang, Xiaodong Li, Shurong China Univ Petr Coll Informat & Control Engn Dongying 257061 Peoples R China

ISBN: (纸本)1424403316

A time nodes optimization method is presented for the solution of optimal control problems (OCP) using control vector parameterization (CVP). The control variable in each time interval is approached by a function of time nodes parameters and other decision parameters. The infinite dimensional optimal control problems were approximated into nonlinear programming (NLP) problems, the gradient of which can be analytically obtained. The NLP problems were solved and resulted in non-uniform time grid. Two cases of optimal control problem were solved by the proposed methodology. One is OCP of an ODE system and the superior results are given comparing with the fixed time grid method. Another is optimal injection strategy determination of polymer flooding, which is a sort of OCP constrained to satisfy PDEs. The efficiency is illustrated for solving this kind of problem by the given method.

关键词： control vector parameterization time nodes optimal control

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Dynamic optimization using a wavelet based adaptive control vector parameterization strategy

Dynamic optimization using a wavelet based adaptive control ...

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7th International Symposium on Process Systems Engineering

作者： Binder, T Cruse, A Villar, CAC Marquardt, W Rhein Westfal TH Aachen Lehrstuhl Prozesstech D-52056 Aachen Germany Col San Pedro Dept Ingn Elect San Pedro Zacatenco Mexico

关键词： dynamic optimization large scale systems adaptive mesh refinement control vector parameterization single shooting wavelets

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Gaussian Discretization-based Non-uniform control vector parameterization for Terminal Constrained Hypersonic Unmanned System trajectory Optimization

Gaussian Discretization-based Non-uniform Control Vector Par...

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Chinese Automation Congress (CAC)

作者： Liu, Hang Teng, Heng Qiu, Guoqing Liu, Ping Yang, Jinfeng Chongqing Univ Posts & Telecommun Coll Automat Chongqing Peoples R China Chongqing Acad Metrol & Qual Inspect Chongqing Peoples R China Chongqing Jianzhu Coll Dept Track & Elect Engn Chongqing Peoples R China

ISBN: (纸本)9781728176871

Since the hypersonic vehicle has a strong sensitivity to the initial parameter values during the trajectory optimization process, a control vector parameterization method based on Gaussian distribution time nodes is proposed, and related solutions are given. By solving the zero point of the Legendre polynomial, the time nodes with Gaussian distribution in the entire control time domain are obtained. Then the control vector is parameterized by using the obtained new time grid, and a high-quality control parameterization strategy is achieved. The numerical results show that the proposed method can increase the performance index of downrange and flight time of hypersonic unmanned system.

关键词： Gaussian discretization control vector parameterization Hypersonic reentry trajectory Terminal Constraints

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State Difference Sensitivity-based control vector parameterization Refinement Approach for Optimal control Problems

State Difference Sensitivity-based Control Vector Parameteri...

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Chinese Automation Congress (CAC)

作者： Qiu, Guoqing Liu, Hang Nie, Chuanjie Fan, Li Liu, Ping Chongqing Univ Posts & Telecommun Chongqing Peoples R China

ISBN: (纸本)9781728140940

To improve the optimization performance of control vector parameterization (CVP) method for optimal control problems, a refinement CVP method based on the state difference sensitivity is proposed. According to the influence of the state vector on the control vector, the state difference of the adjacent time grid nodes makes the control vector sensitive, so new time grid nodes can be selected. Finally, the control parameters obtained with the non-uniform grid are analyzed accordingly. A new NLP problem is obtained with the refined time grid and simulation tests are carried out on a classical optimal control *** results show that the proposed method can effectively shorten the calculation time and increase the calculation accuracy compared with the traditional CVP method.

关键词： control vector parameterization State Difference Sensitivity time grid optimal control

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Establishment of UAV Formation Flight Using control vector parameterization and Sequential Convex Programming 35

Establishment of UAV Formation Flight Using Control Vector P...

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第35届中国控制会议

作者： GUO Juan CHU Jing YAN Jie Northwestern Polytechnical University

ISBN: (纸本)9781509009107

Formation flight of multiple Unmanned Aerial Vehicles(UAVs) could provide an effective, efficient yet low cost alternative to existing technologies. This paper addresses the energy-optimal establishment of UAV formation flight that shall satisfy final configuration constraints. First, the problem of formation establishment is formulated as an energy-optimal control problem which is constrained by the nonlinear dynamics. Then, the optimal control problem is solved using a direct *** this direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach. After that, the sequential convex programming(SCP) technology is employed to derive the optimal solution. Essentially, each instance of SCP is a quadratic programming problem subject to linear constraints that can be solved very efficiently. In the end, the proposed method is applied to the establishment of V formation for three UAVs, where the free open source solver CVX is exploited. By comparison with the global optimization technique provided in MATLAB, the solution converges very fast to the global minimum.

关键词： UAV formation flight Optimal control control vector parameterization Sequential Convex Programming

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Dynamic Optimization using control vector parameterization with State Transition Algorithm 36

Dynamic Optimization using Control Vector Parameterization w...

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第36届中国控制会议

作者： Miao Huang Xiaojun Zhou Chunhua Yang Weihua Gui School of Information Science and Engineering Cental South University

ISBN: (纸本)9781538629185

In real-world applications,a majority of optimization problems belong to dynamic optimization,which involves optimization over time and whose underlying space is *** this paper,a novel dynamic optimization technique based on state transition algorithm(STA) is investigated to solve dynamic optimization problems(DOPs).Firstly,an infinite dynamic optimization problem is converted into a finite nonlinear programming problem(NLP) based on the control vector parameterizations(CVP),in which,instead of discretizing both state and control variables,only the control profiles are approximated by piecewise constant ***,a stochastic global method is proposed to solve the resulting nonlinear programming problem based on state transition *** applying it in two well-known dynamic optimization instances,simulation results show that the proposed approach is able to obtain similar or even better performance indicators compared with other methods in terms of computational cost,solution accuracy and stability.

关键词： State transition algorithm dynamic optimization control vector parameterization

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Asynchronous switching and sparse discretization with time scaling for control vector parameterization optimal control

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ENGINEERING OPTIMIZATION 2024年

作者： Wang, Hainan Gatzke, Edward P. Univ South Carolina Coll Engn & Comp Dept Chem Engn Columbia SC 29208 USA

This work introduces a novel approach for solving open-loop Optimal control Problems (OCPs) using multiple time grids, sparse discretization and a time scaling transformation. control vector parameterization (CVP) method parameterizes control variables to create a finite-dimensional problem. The Variable Time Nodes control vector parameterization (VTNCVP) discretization strategy allows each control component an independent time grid, offering enhanced input design flexibility and potentially yielding improved outcomes. A novel time scaling technique for OCPs with multiple time grids is presented that is easier to comprehend than existing methods and can circumvent some numerical difficulties. Additionally, Multiple Grid (MG)-Sparse Variable Time Nodes (MG-SVTN) is presented. This novel discretization strategy employs asynchronous switching with user-specified numbers of subdivisions for input controls, potentially yielding comparable objective function values to VTNCVP while reducing the dimensionality of decision variables. Two example problems with path constraints are solved using the methods.

关键词： Nonlinear optimal control control vector parameterization asynchronous time grid time scaling transformation sparse discretization method

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An incremental dimensionality-expended optimization strategy based control vector parameterization

An incremental dimensionality-expended optimization strategy...

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第35届中国过程控制会议

作者： Shiqing Liang Yonggang Li Shulong Yin Central South University School of automation

The control vector parameterization(CVP) is one of the most commonly used numerical methods for solving optimal control problems in chemical engineering processes. However, one of its main drawbacks is its low computational efficiency,especially when discretize control profiles piecewise on a fine grid, leading to a high-dimensional nonlinear optimization *** improve the computational efficiency of the CVP method, this paper proposes an optimization strategy that expands the dimensions gradually. First, the high-dimensional optimization problem is initially simplified into a low-dimensional form to facilitate rapid resolution. Subsequently, the optimized low-dimensional solution is gradually extended to higher dimensions to enhance solution accuracy. This strategy is applied to three classic chemical engineering problems and compared with different methods. Simulation results demonstrate that this strategy effectively enhances the efficiency of numerical solving for optimal control in chemical engineering processes.

关键词： control vector parameterization optimal control process control

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Parameter estimation in kinetic models for large scale biotechnological systems with advanced mathematical programming techniques

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BIOCHEMICAL ENGINEERING JOURNAL 2014年 83卷 104-115页

作者： Di Maggio, Jimena Paulo, Cecilia Estrada, Vanina Perotti, Nora Diaz Ricci, Juan C. Soledad Diaz, M. UNS CONICET Planta Piloto Ingn Quim PIAPIQUI RA-8000 Bahia Blanca Buenos Aires Argentina Consejo Nacl Invest Cient & Tecn Planta Piloto Proc Ind Microbiol PROIMI RA-4000 San Miguel De Tucuman Tucuman Argentina UNT CONICET Inst Super Invest Biol INSIBIO RA-4000 San Miguel De Tucuman Tucuman Argentina

In the present work, we formulate parameter estimation problems for kinetic models of large-scale dynamic biotechnological systems. We propose dynamic models of increasing complexity for metabolic networks and continuous bioreactors. The differential algebraic equations (DAE) system for the metabolic network represent the glycolysis, the phosphotransferase system and the pentose-phosphate pathway of Escherichia coli, with modifications proposed for several enzyme kinetics. The most sensitive parameters have been ranked by performing global sensitivity analysis on the dynamic metabolic network. Since the kinetic parameters for the enzymes have been obtained from in vitro experiments, the formulation of a detailed kinetic model for the metabolic network allows parameter adjustment for in vivo conditions. We formulate an unstructured non-segregated model for a chemostat to study the dynamic response to a glucose pulse in a continuous culture of E. coli. Moreover, we perform parameter estimation by formulating a maximum likelihood problem, subject to the DAE systems, within a control vector parameterization approach. Nine kinetic parameters in the metabolic network model have been estimated with good agreement with published experimental data. For the bioreactor model, seven parameters have been tuned based on experimental data obtained in this work. Numerical results show a good agreement between the observed data and the predicted profiles. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Dynamic metabolic network Dynamic optimization control vector parameterization

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