A sequential computational approach to optimal control problems for differential-algebraic systems based on efficient implicit Runge–Kutta integration

Jiang, Canghua; Xie, Kai; Yu, Changjun; Yu, Ming; Wang, Hai; He, Yigang; Teo, Kok Lay

doi:10.1016/j.apm.2017.05.015

Cited by 13 publications

(43 citation statements)

References 10 publications

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“…It is known that integral computations could be time-consuming, especially for complicated mathematical functions. Thus, in this case numerical approximations provide acceptable solutions within a short execution time 29 …”

Section: Methodsmentioning

confidence: 99%

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Comparison of an in-house developed monitor unit double-check program for 3D conformal radiation therapy and treatment planning system verification

Slassi

Ouabi²,

Khayati

2019

J Radiother Pract

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AimThe treatment planning system (TPS) plays a key role in radiotherapy treatments; it is responsible for the accurate determination of the monitor unit (MU) needed to be delivered to treat a patient with cancer. The main goal of radiotherapy is to sterilise the tumour; however, any imprecise dose delivered could lead to deadly consequences. The TPS has a quality assurance tool, an independent program to double check the MU, evaluate patient plan correctness and search for any potential error.Materials and methodsIn this work, a comparison was carried out between a MU calculated by TPS and an independent in-house-developed monitor unit calculation program (MUCP). The program, written in Cplusplus (C++ Object-Oriented), requires a database of several measured quantities and uses a recently developed physically based method for field equivalence calculation. The ROOT CERN data analysis library has been used to establish fit functions, to extend MUCP use to a variety of photon beams. This study presents a new approach to checking MU correctness calculated by the TPS for a water-like tissue equivalent medium, using our MUCP, as the majority of previous studies on the MU independent checks were based on the Clarkson method. To evaluate each irradiated region, four calculation points corresponding to relative depths under the water phantom were tested for several symmetric, asymmetric, irregular symmetric and asymmetric field cases. A comparison of MU for each radiation fields from readings of the TPS and the MUCP was undertaken.ResultsA satisfactory agreement has been obtained and within the required standards (3%). Additional experimental measurements of dose deposited in a water phantom showed a deviation of <1·6%.FindingsThe MUCP is a useful tool for basic and complex MU verification for 3D conformal radiation therapy plans.

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Section: Methodsmentioning

confidence: 99%

“…Thus, in this case numerical approximations provide acceptable solutions within a short execution time. 29 We used MATLAB software (MathWorks, Inc., Natick, MA, USA) to compute the integrals. The MATLAB/C + + platform was established by linking required MATLAB libraries to our program.…”

Section: The Mucpmentioning

confidence: 99%

Comparison of an in-house developed monitor unit double-check program for 3D conformal radiation therapy and treatment planning system verification

Slassi

Ouabi²,

Khayati

2019

J Radiother Pract

View full text Add to dashboard Cite

show abstract

“…Before the iterative solution, the original boundary conditions Equation (11) need to be considered. To impose the boundary conditions, the equations and Jacobian matrix need to be modified.…”

Section: Iterative Solution Methods Of Discrete Equationsmentioning

confidence: 99%

“…For the initial boundary conditions x (0) = x 0 in Equation ( 11), substituting x 0 in the equations Equation (47) by x 0 , that is, the subvector of F is modified as F [1∶nx] = F 1 1 − x 0 . For the terminal boundary conditions in Equation (11), two cases need to be considered respectively:…”

Section: Iterative Solution Methods Of Discrete Equationsmentioning

confidence: 99%

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A symplectic indirect approach for a class of nonlinear optimal control problems of differential‐algebraic systems

Shi

Peng

Wang

et al. 2021

Intl J Robust & Nonlinear

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Differential-algebraic equations (DAEs) can model constrained dynamical systems and processes from practical engineering. Therefore, research on nonlinear optimal control problems of DAEs is of theoretical significance for optimal control of constrained systems, which can generate reference trajectories and control inputs for online control strategies. In terms of the numerical solution of this type of problem, research on indirect numerical methods is still insufficient and less research focuses on symplectic-preserving methods. In this article, a symplectic indirect approach is proposed for optimal control problems subject to index-1 DAEs. Necessary conditions of the optimal control problem constitute a Hamiltonian boundary value problem (HBVP) and there exists a symplectic structure in the Hamiltonian system. In the proposed approach, based on specified properties of generating functions, discrete equations can preserve the symplectic structure of the Hamiltonian system. In the iterative solution, the Jacobian matrices of the discrete equations are sparse and symmetric, which are very significant to save memory and improve efficiency in practical computation. In numerical examples, the proposed approach can provide highly accurate state variables and control inputs with fewer iterations. More accurate cost functional can be obtained. Problems from the chemistry process also can be solved effectively, it verifies the problem-solving ability of the proposed approach. K E Y W O R D Sconstrained systems, differential-algebraic equations, nonlinear optimal control, symplectic methods INTRODUCTIONOriginating from practical engineering applications such as motion planning of robots and optimal strategies of processes, optimal control problems 1-4 have been widely researched in the past decades. Generally, there are a defined cost functional and dynamical constraints in the optimal control problem. The aim is to find optimal state variables and control inputs that fulfill dynamical constraints and minimize the cost functional. The cost functional is a scalar function with respect to state variables and control inputs, which is defined according to practical requirements. For example, the task is to 2712

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A symplectic direct method for motion-driven optimal control of mechanical systems

Shi

Peng

Wang

et al. 2022

Communications in Nonlinear Science and Numerical Simulation

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A sequential computational approach to optimal control problems for differential-algebraic systems based on efficient implicit Runge–Kutta integration

Cited by 13 publications

References 10 publications

Comparison of an in-house developed monitor unit double-check program for 3D conformal radiation therapy and treatment planning system verification

Comparison of an in-house developed monitor unit double-check program for 3D conformal radiation therapy and treatment planning system verification

A symplectic indirect approach for a class of nonlinear optimal control problems of differential‐algebraic systems

A symplectic direct method for motion-driven optimal control of mechanical systems

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