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The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.

The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.

It will promote the accuracy of multivariate grey incidence model.

Higher education has a vital role to play in shaping the way in which future generations learn to cope with the complexities of sustainable development. Universities and higher education institutions educate highly qualified graduates and responsible citizens able to meet the needs of all sectors of human activity; they provide opportunities for higher learning and for learning throughout life; they advance, create and disseminate knowledge through research and provide, as part of their service to the community, relevant expertise to assist societies in cultural, social and economic development; they contribute to the development and improvement of education at all levels, including through the training of teachers. The objective of this study is to examine the relationship between higher education and economic growth in Iran.

First, a baseline survey analysis of Iran supported by tables and figures was conducted. Secondly, by using multivariable time series data on the variables: annual logarithmic gross domestic product, physical capital (K), human capital, research expenditures (R) and by using an autoregressive distributed lag (ARDL) model, the long‐ and short‐run relationship between the growth and higher education variable was investigated. The following steps were followed: test of a dynamic ARDL model, CUSUM and CUSUMQ test for stability, long‐run relationship and ECM test.

The results indicated that the higher education variable had a positive effect on the economic growth of Iran in both the short and long run.

The research in this paper has implications for government policy makers responsible for investment in higher education.

The purpose of this paper is to propose an identification algorithm to obtain generalized attitude model (GAM) of satellites in on‐orbit environment, which includes missing attitude data and multi‐noise. The identified GAM and noise model are the basis of attitude control and state estimation on‐orbit.

To cope with noises contaminating both input and output of attitude model, the errors‐in‐variables model is transformed into a traditional Box‐Jenkins model according to the attitude control loop. The wavelet denoising (WD) technique is helpful to predict the missing output data using the identified GAM.

By the numerical simulation, it is verified that the proposal accompanied with WD has a faster prediction capability than that of the algorithm without WD. As a result, the proposed approach is suitable to attitude model identification of on‐orbit satellites.

This identification algorithm can deal with two kinds of on‐orbit conditions and has a fast parameter convergent rate. Therefore, it has a practical application value in on‐orbit environment.

The purpose of this study is to make a prediction of the R&D output of China from the perspective of R&D institutions and put forward a set of policy recommendations for further development of the science and technology in China.

In this paper, an improved discrete grey multivariable model is proposed, which takes both the interaction effects and the accumulative effects into account. As the current research on China's R&D activities is generally based on the perspective of universities or industrial enterprises above designated size while few studies put their focus on R&D institutions, this paper applies the proposed model to carry out an empirical analysis based on the data of China's R&D institutions from 2009 to 2019. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of the R&D output in China's R&D institutions is conducted into a future horizon from 2020 to 2023 by using the model.

The results indicate that China's R&D institutions have a good development trend and broad prospects, which is closely related to China's long-term investment in science and technology. Additionally, the R&D inputs of China possess obvious interaction effects and accumulative effects.

The paper considers the interaction effects and the accumulative effects of R&D inputs simultaneously and proposes an improved discrete grey multivariable model, which fills the gap in previous studies.

With the development of economy, China’s OFDI constantly increase in recent year. Meanwhile, OFDI has spillover effect on economic development and technological development of home country. Thus, accurate OFDI prediction is a prerequisite for the effective development of international investment strategies. The purpose of this paper is to predict China’s OFDI accurately using a novel multivariable grey prediction model with Fourier series.

This paper applied a multivariable grey prediction model, GM(1,N), to forecast China’s OFDI. In order to improve the prediction accuracy and without changing local characteristics of grey model prediction, this paper proposed a novel grey prediction model to improve the performance of the traditional GM(1,N) model by combining with residual modification model using GM(1,1) model and Fourier series.

The coefficients indicate that the export and GDP have positive influence on China’s OFDI, and, according to the prediction result, China’s OFDI shows a growing trend in next five years.

This paper proposed an effective multivariable grey prediction model that combined the traditional GM(1,N) model with a residual modification model in order to predict China’s OFDI. Accurate forecasting of OFDI provides reference for the Chinese Government to implement international investment strategies.

The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

This study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.

In this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.

The results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.

The paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.

High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model.

Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships.

The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021.

The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models.

The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning.

A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

The purpose of this paper is to examine the effectiveness of an improved dummy variables control grey model (DVCGM) considering the hysteresis effect of government policies in China's energy intensity (EI) forecasting.

Energy consumption is considered as an important driver of economic development. China has introduced policies those aim at the optimization of energy structure and EI. In this study, EI is forecasted by an improved DVCGM, considering the hysteresis effect of energy-saving policies of the government. A nonlinear optimization method based on particle swarm optimization (PSO) algorithm is constructed to calculate the hysteresis parameter. A one-step rolling mechanism is applied to provide input data of the prediction model. Grey model (GM) (1, N), DVCGM (1, N) and ARIMA model are applied to test the accuracy of the improved DVCGM (1, N) model prediction.

The results show that the improved DVCGM provides reliable results and works well in simulation and predictions using multivariable data in small sample size and time-lag virtual variable. Accordingly, the improved DVCGM notes the hysteresis effect of government policies and significantly improves the prediction accuracy of China's EI than the other three models.

This study estimates the EI considering the hysteresis effect of energy-saving policies in China by using an improved DVCGM. The main contribution of this paper is to propose a model to estimate EI, considering the hysteresis effect of energy-saving policies and improve forecasting accuracy.