Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Paiva, Luís Tiago; Fontes, Fernando A. C. C.

doi:10.1016/j.protcy.2014.10.226

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…One of such techniques is reported in [190], which proposed an adaptive time-mesh algorithm based on refinement criteria. The criteria use the information of the adjoint multipliers and involve multi-level refinement unlike earlier works [191], [192] and validates the results by applying the Maximum Principle of Pontryagin.…”

Section: Figure 24supporting

confidence: 59%

Robotics Inspired Renewable Energy Developments: Prospective Opportunities and Challenges

et al. 2019

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The domain of Robotics is a good partner of renewable energy and is becoming critical to the sustainability and survival of the energy industry. The multi-disciplinary nature of robots offers precision, repeatability, reliability, productivity and intelligence, thus rendering their services in diversified tasks ranging from manufacturing, assembling, and installation to inspection and maintenance of renewable resources. This paper explores applications of real robots in four feasible renewable energy domains; solar, wind, hydro, and biological setups. In each case, existing state-of-the-art innovative robotic systems are investigated that have the potential to create a difference in the corresponding renewable sector in terms of reduced set-up time, lesser cost, improved quality, enhanced productivity and exceptional competitiveness in the global market. Instrumental opportunities and challenges of robot deployment in the renewable sector are also discussed with a brief case study of Saudi Arabia. It is expected that the wider dissemination of the instrumental role of robotics in renewable energy will contribute to further developments and stimulate more collaborations and partnerships between professionals of robotics and energy communities.INDEX TERMS Applied robotics, automation in renewable energy, mobile robots, robotic manipulators, solar PV module, wind turbines.

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Section: Figure 24supporting

confidence: 59%

Robotics Inspired Renewable Energy Developments: Prospective Opportunities and Challenges

et al. 2019

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“…This problem was addressed in many studies using different formulations. For example, but not limited to, Paiva and Fontes (2014) presented a mesh-refinement strategy based on a block-structured adaptive mesh refinement method that is modified by Nikiforakis (2009) for solving continuous time nonlinear openloop. Bartl et al (2011) proposed a time derivative analysis within the quasi-sequential approach and derived a finite element placement strategy.…”

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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“…Liu et al used a novel penalty method to deal with nonlinear dynamic optimization problems with inequality path constraints [2]. Paiva and Fontes studied the adaptive mesh refinement algorithms which allow a nonuniform node collocation and apply a time mesh refinement strategy based on the local error into practical problems [3]. Zhao and Tsiotras introduced an efficient and simple method based on density (or monitor) functions, which have been used extensively for grid refinement.…”

Section: Introductionmentioning

confidence: 99%

An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

Gong

Jiang

Zhang

et al. 2017

Mathematical Problems in Engineering

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The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.

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Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Cited by 6 publications

References 12 publications

Robotics Inspired Renewable Energy Developments: Prospective Opportunities and Challenges

Robotics Inspired Renewable Energy Developments: Prospective Opportunities and Challenges

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

An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

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