An Approach to Determining the Number of Time Intervals for Solving Dynamic Optimization Problems

Lazutkin, Evgeny; Geletu, Abebe; Li, Pu

doi:10.1021/acs.iecr.7b03361

Cited by 8 publications

(6 citation statements)

References 55 publications

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“…Optimal values for the decision variables (η*, x*(t), u*(t), y*(t)) are obtained from the solution of Equation (11). Note that function T i is not constrained, as shown in Equation (11h).…”

Section: Stage 2: Integrated Design and Control Problemmentioning

confidence: 99%

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

Palma-Flores

Ricardez‐Sandoval

2023

AIChE Journal

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In this work, we propose a /methodology for the selection and refinement of finite elements for the integration of process design and control. The proposed methodology is based on the selection criteria of the Hamiltonian function through the implementation of the Pontryagin's minimum principle. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes, which is exploited in this work for the refinement of the discretization. Furthermore, the residuals at noncollocation points are evaluated to estimate the collocation error, this is used as a second refinement criterion in the proposed framework. The methodology is illustrated using two case studies featuring a reaction system with two CSTRs in series and the Williams–Otto reactor, respectively. The results showed that an accurate selection of the finite elements return economically attractive designs with fewer elements than those obtained with equidistributed finite element strategies.

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Section: Stage 2: Integrated Design and Control Problemmentioning

confidence: 99%

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

Palma-Flores

Ricardez‐Sandoval

2023

AIChE Journal

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“…Since the input MB scheme considers more state and path constraints, its time for solving QP is slightly higher than that of nonuniform grid scheme. It is interesting to compare performance of a specific parameterization of scheme B that shows similar computational time to that of scheme C. This can be achieved by increasing the number of intervals for non-uniform grid NMPC (scheme B) to M = 42 with I =[0, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,28,32,35,37,40,42,44,46,48,50,52,55,60,65,70,75,80] The state and control trajectories are shown in Fig. 4 and the KKT values are shown in Fig.…”

Section: A Control Of An Inverted Pendulummentioning

confidence: 99%

“…However, the reduction of the number of nodes comes at the cost of a loss of discretization accuracy. To deal with this issue, the number of discretization intervals has been determined a priori off-line while guaranteeing an upper limit of the discretization error in [2]. In addition, adaptive time-mesh refinement techniques have been proposed to improve computation efficiency while maintaining a certain degree of discretization accuracy [3], [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Chen

Scarabottolo²,

Bruschetta³

et al. 2020

IET Control Theory & Applications

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Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretization steps. In this paper, we focus on developing computationally efficient MB schemes for multiple shooting based nonlinear model predictive control (NMPC). The degrees of freedom of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretization accuracy and level of sparsity is maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretization nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimization accuracy and constraints fulfillment is shown by means of simulations with two different problems.

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“…Zhu et al (2018) proposed a method by combining the domain decomposition method and the collocation method. Lazutkin et al (2018) proposed a bi-level approach for a priori error estimation by taking the effect of both the discretization scheme and the operating condition into account. Biegler et al (1986) with other scholars (e.g.…”

Section: Introductionmentioning

confidence: 99%

Choosing the number of time intervals for solving a model predictive control problem of nonlinear systems

Tamimi

2021

Transactions of the Institute of Measurement and Control

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Model predictive control (MPC) is a control strategy that can handle state and control multi-variables at same time. To use the MPC using direct methods for solving the a dynamic optimization problem, one needs, for example, to transform the optimization problem into a nonlinear programming (NLP) problem by dividing the prediction horizon into equal time intervals. In this work, we suggest a tool and procedures for helping to choose a ‘compromise’ number of time intervals with a needed accuracy, objective cost, number of turned NLP iterations and computational time. On the other hand, we offer a simplified nonlinear program to ensure the convergence of a class of finite optimal control problem by modifying the state box constraints. In particular, a special type of box constraints were used to the constrained optimal control problem to enforce the state trajectories to reach the desired stationary point. These box constraints are characterized by some parameters that are easily optimized by our proposed nonlinear program. Our proposed tools are tested using two case studies; nonlinear continuous stirred tank reactor (CSTR) and nonlinear batch reactor.

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An Approach to Determining the Number of Time Intervals for Solving Dynamic Optimization Problems

Cited by 8 publications

References 55 publications

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

Selection and refinement of finite elements for optimal design and control: A Hamiltonian function approach

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Choosing the number of time intervals for solving a model predictive control problem of nonlinear systems

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