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) met...
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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.
control vector parameterization method is the most commonly used numerical computation method in solving dynamic programming problems. However, to balance the expected trajectory and the computational cost, this metho...
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control vector parameterization method is the most commonly used numerical computation method in solving dynamic programming problems. However, to balance the expected trajectory and the computational cost, this method faces difficulties in dividing the optimal discretization time grid. In this paper, we propose an effective control approach for non-uniform adaptive grid division. By analyzing the slope change trend of the control parameter, time nodes are adaptively refined by merging time grids with gentle slopes to remove unnecessary time nodes and adding time nodes to time grids with steep slopes to improve function approximation accuracy. Eventually, we obtain an adaptive time grid division method under which the trajectory of discretization control parameter is more approximate to the optimal control trajectory. Under the condition of intuitive slope information, the proposed method can achieve better performance with fewer optimization parameters and shorter computation time. Finally, the proposed method is applied to solve a classic optimal control problem and the obtained results are compared with the traditional control vector parameterization method. By comparison through the example, our proposed method can overcome the contradiction between approximation accuracy and computational cost in control vector parameterization method and improve the optimization efficiency.
control vector parameterization is a mainstream numerical approach for solving dynamic programming problems. By discretizing the entire time domain into a grid of time nodes, an infinite-dimensional optimal control pr...
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control vector parameterization is a mainstream numerical approach for solving dynamic programming problems. By discretizing the entire time domain into a grid of time nodes, an infinite-dimensional optimal control problem can be transformed into a finite-dimensional static optimization problem. Despite the attractive advantages of high solution accuracy and ease of implementation of control vector parameterization, the rationality of time grid partitioning significantly influences the efficiency of the solution and the approximating accuracy of the optimal control trajectory. In the traditional control vector parameterization method, the time grid is typically set beforehand and remains static in the optimization process, which has a direct impact on how closely the solution result approximates the optimal control trajectory. To address the conflict of accurate approximations and computational time, we propose a slope-based automatic identification and optimization of key time nodes method for adaptive control vector parameterization, which not only optimizes merging and inserting time nodes but also incorporates automatic identification of key time nodes. Through a simulation example, we verify that this improved method can reduce computation time, enhance approximation accuracy, and achieve higher optimization efficiency.
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 computa...
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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.
In this paper, a novel strategy for finding the optimal operation profiles for nonlinear dynamic processes is developed. Based on the direct sequential stochastic framework for dynamic optimization, this work proposes...
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In this paper, a novel strategy for finding the optimal operation profiles for nonlinear dynamic processes is developed. Based on the direct sequential stochastic framework for dynamic optimization, this work proposes a technique based on Fourier series for the control vector parameterization, as an alternative to the traditional methods. This approach has the advantage of choosing a high degree of smoothness to avoid sharp changes for the input variables, which is preferred in most chemical and biological processes. On the other hand, when several arcs are present in the qualitative optimal profile, the number of parameters can be increased for a better approximation. The proposed strategy was applied to four well-studied nonlinear processes, covering batch and fed-batch reactors, and multi-input systems. The algorithm was tested through simulations. Good performances were obtained in comparison to some previous results available in the literature. (C) 2020 Elsevier Ltd. All rights reserved.
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 p...
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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 controlvector is parameterized by using the obtained new time grid, and a high-quality controlparameterization 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.
A novel optimal approach named invasive weed optimization-control vector parameterization (IWO-CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear pr...
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A novel optimal approach named invasive weed optimization-control vector parameterization (IWO-CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear programming (NLP) problem and an IWO algorithm is then applied to tackle the NLP problem. To improve efficiency, a new adaptive dispersion IWO-based approach (ADIWO-CVP) is further suggested to maintain the exploration ability of the algorithm throughout the entire searching procedure. Several classic chemical dynamic optimization problems are tested and detailed comparisons are carried out among ADIWO-CVP, IWO-CVP, and other methods. The research results demonstrate that ADIWO-CVP not only is efficient, but also outperforms IWO-CVP in terms of both accuracy and convergence speed.
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 inf...
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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 controlvector, the state difference of the adjacent time grid nodes makes the controlvector 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.
High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control q...
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High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost;meanwhile, the control quality is efficiently improved. (C) 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Dynamic optimization is a very effective way to increase the profitability or productivity of bioprocesses. As an important method of dynamic optimization, the control vector parameterization (CVP) approach needs to s...
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Dynamic optimization is a very effective way to increase the profitability or productivity of bioprocesses. As an important method of dynamic optimization, the control vector parameterization (CVP) approach needs to select an optimal discretization level to balance the computational cost with the desired solution quality. A new sensitivity-based adaptive refinement method is therefore proposed, by which new time grid points are only inserted where necessary and unnecessary points are eliminated so as to obtain economic and effective discretization grids. Moreover, considering that traditional refinement methods may cost a lot to get the high-quality solutions of some bioprocess problems, whose performance indices are sensitive to some significant time points, an optimization technique is further proposed and embedded into the new sensitivity-based CVP approach to efficiently solve these problems. The proposed methods are applied to two wellknown bioprocess optimization problems and the results illustrate their effectiveness.
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