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An Introduction to Algorithmic Finance, Algorithmic Trading and Blockchain
Type: Book
ISBN: 978-1-78973-894-0

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Publication date: 15 December 1998

J.D. Addison and B.G. Heydecker

This paper investigates the temporal inflow profile that minimises the total cost of travel for a single route. The problem is formulated to consider the case in which the…

Abstract

This paper investigates the temporal inflow profile that minimises the total cost of travel for a single route. The problem is formulated to consider the case in which the total demand to be serviced is fixed. The approach used here is a direct calculation of the first order variation of total system cost with respect to variations in the inflow profile. Two traffic models are considered; the bottleneck with deterministic queue and the kinematic wave model. For the bottleneck model a known solution is recovered. The wave model proves more difficult and after eliminating the possibility of a smooth inflow profile the restricted case of constant inflow is solved. As the space of possible profiles is finite dimensional in this case, the standard techniques of calculus apply. We establish a pair of equations that are satisfied simultaneously by the optimal inflow and time of first departure.

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Mathematics in Transport Planning and Control
Type: Book
ISBN: 978-0-08-043430-8

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An Introduction to Algorithmic Finance, Algorithmic Trading and Blockchain
Type: Book
ISBN: 978-1-78973-894-0

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Grey Systems: Theory and Application, vol. 8 no. 4
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 15 July 2021

Sandang Guo and Yaqian Jing

In order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati…

Abstract

Purpose

In order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.

Design/methodology/approach

By combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.

Findings

Based on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.

Practical implications

Due to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.

Originality/value

The main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

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Grey Systems: Theory and Application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 14 June 2021

Xiaofeng Liu, Jiahong Xu and Yuhong Liu

The purpose of this research on the control of three-axis aero-dynamic pendulum with disturbance is to facilitate the applications of equipment with similar pendulum…

Abstract

Purpose

The purpose of this research on the control of three-axis aero-dynamic pendulum with disturbance is to facilitate the applications of equipment with similar pendulum structure in intelligent manufacturing and robot.

Design/methodology/approach

The controller proposed in this paper is mainly implemented in the following ways. First, the kinematic model of the three-axis aero-dynamic pendulum is derived in state space form to construct the predictive model. Then, according to the predictive model and objective function, the control problem can be expressed a quadratic programming (QP) problem. The optimal solution of the QP problem at each sampling time is the value of control variable.

Findings

The trajectory tracking and point stability tests performed on the 3D space with different disturbances are validated and the results show the effectiveness of the proposed control strategy.

Originality/value

This paper proposes a nonlinear unstable three-axis aero-dynamic pendulum with less power devices. Meanwhile, the trajectory tracking and point stability problem of the pendulum system is investigated with the model predictive control strategy.

Details

Assembly Automation, vol. 41 no. 3
Type: Research Article
ISSN: 0144-5154

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Article
Publication date: 30 June 2021

Umer Saeed

The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

Abstract

Purpose

The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

Design/methodology/approach

The author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations.

Findings

The author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method.

Originality/value

Many scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author’s knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations.

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Article
Publication date: 14 June 2021

Ruirui Shao, Zhigeng Fang, Liangyan Tao, Su Gao and Weiqing You

During the service period of communication satellite systems, their performance is often degraded due to the depletion mechanism. In this paper, the grey system theory is…

Abstract

Purpose

During the service period of communication satellite systems, their performance is often degraded due to the depletion mechanism. In this paper, the grey system theory is applied to the multi-state system effectiveness evaluation and the grey Lz-transformation ADC (availability, dependability and capability) effectiveness evaluation model is constructed to address the characteristics of the communication satellite system such as different constituent subsystems, numerous states and the inaccuracy and insufficiency of data.

Design/methodology/approach

The model is based on the ADC effectiveness evaluation method, combined with the Lz transformation and uses the definite weighted function of the three-parameter interval grey number as a bridge to incorporate the possibility of system performance being greater than the task demand into the effectiveness solution algorithm. At the same time, using MATLAB (Matrix laboratory) to solve each state probability, the same performance level in the Lz transform is combined. Then, the system effectiveness is obtained by Python.

Findings

The results show that the G-Lz-ADC model constructed in this paper can accurately evaluate the effectiveness of static/dynamic systems and certain/uncertain system and also has better applicability in evaluating the effectiveness of the multi-state complex system.

Practical implications

The G-Lz-ADC effectiveness evaluation model constructed in this paper can effectively reduce the complexity of traditional effectiveness evaluation models by combining the same performance levels in the Lz-transform and solving the effectiveness of the system with the help of computer programming, providing a new method for the effectiveness evaluation of the complex MSS. At the same time, the weaknesses of the system can be identified, providing a theoretical basis for improving the system’s effectiveness.

Originality/value

The possibility solution method based on the definite weighted function comparing the two three-parameter interval grey numbers is constructed, which compensates for the traditional calculation of the probability based on numerical values and subjective preferences of decision-makers. Meanwhile, the effectiveness evaluation model integrates the basic theories of three-parameter interval grey number and its definite weighted function, Grey−Markov, grey universal generating function (GUGF), grey multi-state system (GMSS), etc., which is an innovative method to solve the effectiveness of a multi-state instantaneous communication satellite system.

Details

Grey Systems: Theory and Application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 13 July 2021

Abdulsamed Tabak

The purpose of this paper is to improve transient response and dynamic performance of automatic voltage regulator (AVR).

Abstract

Purpose

The purpose of this paper is to improve transient response and dynamic performance of automatic voltage regulator (AVR).

Design/methodology/approach

This paper proposes a novel fractional order proportional–integral–derivative plus derivative (PIλDµDµ2) controller called FOPIDD for AVR system. The FOPIDD controller has seven optimization parameters and the equilibrium optimizer algorithm is used for tuning of controller parameters. The utilized objective function is widely preferred in AVR systems and consists of transient response characteristics.

Findings

In this study, results of AVR system controlled by FOPIDD is compared with results of proportional–integral–derivative (PID), proportional–integral–derivative acceleration, PID plus second order derivative and fractional order PID controllers. FOPIDD outperforms compared controllers in terms of transient response criteria such as settling time, rise time and overshoot. Then, the frequency domain analysis is performed for the AVR system with FOPIDD controller, and the results are found satisfactory. In addition, robustness test is realized for evaluating performance of FOPIDD controller in perturbed system parameters. In robustness test, FOPIDD controller shows superior control performance.

Originality/value

The FOPIDD controller is introduced for the first time to improve the control performance of the AVR system. The proposed FOPIDD controller has shown superior performance on AVR systems because of having seven optimization parameters and being fractional order based.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 24 March 2021

Jawad Ali, Zia Bashir and Tabasam Rashid

The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution…

Abstract

Purpose

The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

Design/methodology/approach

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

Findings

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

Practical implications

A case study concerning the healthcare facilities in public hospital is addressed.

Originality/value

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

Details

Grey Systems: Theory and Application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2043-9377

Keywords

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