Discrete-form time-dependent quadratic programming (DF-TDQP) problem, as a type of time-dependent problems, is prevalent in science and engineering. Currently, there are many studies on the discretization of continuous time-dependent problems despite the fact that researchers have made different breakthroughs using recurrent neural networks (RNNs) in dealing with discrete-form time-dependent problems, relatively limited research has been devoted to the direct discretization approach. To solve the DF-TDQP problem, a novel direct discretization approach is introduced. Based on this approach, the corresponding discrete-form recurrent neurodynamics (DFRN) model is developed. Furthermore, on this basis, a novel enhanced discrete-form recurrent neurodynamics (E-DFRN) model is further established to obtain high-accuracy optimal solutions for such DF-TDQP problems. The accuracy and convergence of both the DFRN model and E-DFRN model are explained through theoretical analysis, and their effectiveness and superiority are validated based on numerical experiments. Finally, the applicability of these models to the tracking tasks of planar manipulators is verified.

Recurrent neural network (RNN) is a neurodynamic method designed to tackle time-varying problems in various technical domains, which are widely derived from scientific research and practical applications. It should be noted that traditional models often lack an effective capability to suppress nonlinear time-varying noise during the design process, and thus may encounter many difficulties in practical applications. This article presents a novel RNN model for solving the continuous time-varying matrix pseudoinverse, which has a significant characteristic of double integral-reinforcing (DIR) term and is termed DIR continuous-time RNN (DIR-CT-RNN) model. Correspondingly, using the discretization formula, a DIR discrete-time RNN (DIR-DT-RNN) is presented for solving the discrete time-varying matrix pseudoinverse. The theoretical results present that the DIR-DT-RNN model converges toward the theoretical solution under the discrete time-unvarying constant (DTU-C) noise or discrete time-varying linear (DTV-L) noise interference. Under the discrete time-varying quadratic (DTV-Q) noise interference, the proposed model converges to a constant that relates to the design parameters. In addition, simulation results, including an application for trajectory tracking of three-link robotic manipulator, which come from practical engineering background, verify the effectiveness and superiority of DIR-DT-RNN model for solving the time-varying matrix pseudoinverse under various types of noise interference.

Discrete time-variant equation systems represent a typical and complex problem across various disciplines. With the increasing complexity of systems in various fields, traditional methods have been unable to effectively deal with the current discrete time-variant equation systems, especially in the dynamic engineering problem. Generally speaking, traditional methods are typically limited to considering discrete time-variant equation systems in ideal state, and there is a lack of deep research about more intricate disturbance states. This paper introduces a new recurrent neural network (RNN) algorithm, termed the discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm, for handling discrete time-variant equation systems (including discrete time-variant linear and nonlinear equation system) under discrete square-time-variant disturbance. Firstly, the continuous-time double-integration-enhanced RNN (CT-DIE-RNN) algorithm is presented for solving discrete time-variant linear and nonlinear equation systems by using double-integral-type error function. Secondly, the corresponding discrete-time RNN algorithm is presented, and the convergence and precision of such an algorithm are theoretically analyzed. Finally, the effectiveness and superiority of the proposed DT-DIE-RNN algorithm for solving discrete time-variant linear and nonlinear equation systems are supported by comparative numerical experiments, and these theoretical results are further verified by robot manipulator applications.Note to Practitioners—Generally speaking, previous algorithms are unable to guarantee the operation of robot manipulator stably with discrete square-time-variant disturbance. In this study, we design a new RNN algorithm which possesses stronger anti-disturbance capability for solving discrete time-variant equation systems, and such the algorithm is applied to the tracking control of robot manipulator. In the discrete-time environment, in order to solve the discrete time-variant problem smoothly and stably, it is necessary to ensure that the error in each time period is within an acceptable range. The basic guidelines of this paper are as follows. First of all, a double-integration RNN algorithm is constructed, i.e., discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm. Then the effectiveness and superiority of the DT-DIE-RNN algorithm are verified by numerical experiment and engineering simulation, respectively. In summary, the proposed RNN algorithm can be seen as a new breakthrough in the research field of discrete-time RNN algorithm.

A series of discrete time-variant matrix inequalities is generally regarded as one of the challenging problems in science and engineering fields. As a discrete time-variant problem, the existing solving schemes generally need the theoretical support under the continuous-time framework, and there is no independent solving scheme under the discrete-time framework. The theoretical deficiency of solving scheme greatly limits the theoretical research and practical application of discrete time-variant matrix inequalities. In this article, new discrete-time recurrent neural network (RNN) algorithms are proposed, analyzed, and investigated for solving different time-variant matrix inequalities under the discrete-time framework, including discrete time-variant matrix vector inequality (discrete time-variant MVI), discrete time-variant generalized matrix inequality (discrete time-variant GMI), discrete time-variant generalized-Sylvester matrix inequality (discrete time-variant GSMI), and discrete time-variant complicated-Sylvester matrix inequality (discrete time-variant CSMI), and all solving processes are based on the direct discretization thought. Specifically, first of all, four discrete time-variant matrix inequalities are presented as the target problems of these researches. Second, for solving such problems, we propose corresponding discrete-time recurrent neural network (RNN) (DT-RNN) algorithms (termed DT-RNN-MVI algorithm, DT-RNN-GMI algorithm, DT-RNN-GSMI algorithm, and DT-RNN-CSMI algorithm), which are different from the traditional DT-RNN design thought because second-order Taylor expansion is applied to derive the DT-RNN algorithms. This creative process avoids the intervention of continuous-time framework. Then, theoretical analyses are presented, which show the convergence and precision of the DT-RNN algorithms. Abundant numerical experiments are further carried out, which further confirm the excellent properties of the DT-RNN algorithms.

Time-variant problems are widespread in science and engineering, and discrete-time recurrent neurodynamics (DTRN) method has been proved to be an effective way to deal with a variety of discrete time-variant problems. However, this DTRN method is usually based on the study of continuous time-variant problems and lacks a direct study of discrete time-variant problems. To solve the abovementioned problem, based on a pioneering direct discretization technique, we study and develop a new DTRN method to solve equality-constrained discrete time-variant nonlinear optimization (EC-DTVNO) problem. Specifically, first, to solve the EC-DTVNO problem, the recent method widely used by researchers is Lagrange multiplier method. By introducing Lagrange multiplier to construct Lagrange function, the objective function and equality constraint are integrated into a discrete time-variant nonlinear system. Then, the corresponding error function is defined, and the corresponding DTRN method for solving the EC-DTVNO problem can be obtained by direct discretization technique. Thereafter, this DTRN method is analyzed theoretically and its convergence is proved. In addition, numerical experiments and application experiments further confirm the effectiveness and superiority of DTRN method.

rgb0.00,0.00,0.00 In recent years, the discrete-time recurrent neural network (DTRNN) model has received growing attention. This fully benefits from the recurrent neural networks (RNNs) that not only have plenty of advantages for solving computing problems in the real-time tracking control but also have the remarkable potential of parallel processing and nonlinear processing. However, there is a general lack of research on the applicability of DTRNN model to handle parallel robot. In addition, the precision is always an important point in real-time tracking control, and most of existing studies generally lack the elaborate researches on the precision analyses. In this article, the corresponding DTRNN model (i.e., general five-instant discretization (FID) formula DTRNN model) with parameter selection method is established. As one of the important theoretical contributions, the dominant term of truncation error of discretization formula and the conditions of maintaining precision of corresponding DTRNN model are proved from the mathematical view strictly. Besides, the influence of the selected parameter for the precision of such a DTRNN model is also analyzed. Finally, the above theoretical analyses are verified in the tracking control experiments of the Stewart platform, which is a widely used and representative parallel robot.

The existing discrete-time neural dynamics methods for solving the multilinear tensor equation (MTE) with$\mathcal {M}$-tensor are all derived from the continuous-time one and depend on the Euler difference formula, which cannot be applied to essentially discrete problems and have low solution accuracy. Moreover, these methods all focus on static problems rather than time-varying ones, and thus may have unsatisfactory performance in applications with time-varying parameters. Additionally, most of these methods fail to handle the MTE with$\mathcal {M}$-tensor under noisy conditions. To remedy these issues, a high-order robust discrete-time neural dynamics (HRDND) method with a directly discrete approach is proposed for solving the time-varying MTE (TMTE) with$\mathcal {M}$-tensor in this article. Theoretical analyses on convergence and robustness are provided to prove that the proposed HRDND method is feasible and effective. Finally, simulative experiments on four time-varying numerical examples and an application derived from the Bellman equation solved by the proposed HRDND method and other four methods are given, whose results illustrate the superiority of the proposed HRDND method.

In recent years, the cable-driven planar robot has made fruitful achievements in many fields, but the related researches are scarce yet in the industrial engineering field. In this article, as a powerful tool for solving discrete time-varying problems, the discrete-time recurrent neural network (DTRNN) is extended to drive the cable-driven planar robot for discrete real-time tracking control, which is derived by a new immediate discretization method, and thus, is termed as ID-DTRNN model. Specifically, first, we present the physical structure and mathematical model of the cable-driven planar robot. Then, the new ID-DTRNN model is proposed and applied for driving such cable-driven planar robot, which bases on the a different way of construction of the traditional DTRNN model. Through numerical experiments, the feasibility, validity, and physical reliability of the ID-DTRNN model for discrete real-time tracking control of the cable-driven planar robot are fully verified. In addition, in the real world, physical experiments of the cable-driven planar robot are presented, which successfully promote the development of physical application of the ID-DTRNN model, and fill the gap of such model in the industrial engineering field.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

In this article, a robust k -winner-take-all ( k -WTA) neural network employing the saturation-allowed activation functions is designed and investigated to perform a k -WTA operation, and is shown to possess enhanced robustness to disturbance compared to existing k -WTA neural networks. Global convergence and robustness of the proposed k -WTA neural network are demonstrated through analysis and simulations. An application studied in detail is competitive multiagent coordination and dynamic task allocation, in which k active agents [among ] are allocated to execute a tracking task with the static m-k ones. This is implemented by adopting a distributed k -WTA network with limited communication, aided with a consensus filter. Simulation results demonstrating the system's efficacy and feasibility are presented.

In this article, the discrete-form time-variant multi-augmented Sylvester matrix problems, including discrete-form time-variant multi-augmented Sylvester matrix equation (MASME) and discrete-form time-variant multi-augmented Sylvester matrix inequality (MASMI), are formulated first. In order to solve the above-mentioned problems, in continuous time-variant environment, aided with the Kronecker product and vectorization techniques, the multi-augmented Sylvester matrix problems are transformed into simple linear matrix problems, which can be solved by using the proposed discrete-time recurrent neural network (RNN) models. Second, the theoretical analyses and comparisons on the computational performance of the recently developed discretization formulas are presented. Based on these theoretical results, a five-instant discretization formula with superior property is leveraged to establish the corresponding discrete-time RNN (DTRNN) models for solving the discrete-form time-variant MASME and discrete-form time-variant MASMI, respectively. Note that these DTRNN models are zero stable, consistent, and convergent with satisfied precision. Furthermore, illustrative numerical experiments are given to substantiate the excellent performance of the proposed DTRNN models for solving discrete-form time-variant multi-augmented Sylvester matrix problems. In addition, an application of robot manipulator further extends the theoretical research and physical realizability of RNN methods.

Lexical simplification (LS) aims at replacing complex words with simpler alternatives. LS commonly consists of three main steps: complex word identification, substitute generation, and substitute ranking. Existing LS methods focus on the contextual information of the complex word in the last step (substitute ranking). However, they miss out the following two facts: (1) The word complexity of a polysemous word is very closely related to its context; (2) The step of substitute generation regardless of the context will inevitably produce a large number of spurious candidates. Therefore, we propose a novel LS system LSBert based on pretrained language model BERT to address the aforementioned issues, which is capable of making use of the wider context when both identifying the words in need of simplification and generating substitute candidates for the complex words. Specifically, LSBert consists of a network for complex word identification by fine-tuning BERT and a network for substitute generation based on BERT. Experimental results show that LSBert performs well in both complex word identification and substitute generation, achieving state-of-the-art results in three benchmarks. To facilitate reproducibility, the code of the LSBert system is available at https://github.com/qiang2100/BERT-LS.

Many time-varying problems have been solved using the zeroing neural network proposed by Zhang et al. In this article, nine types of time-varying problems, namely time-varying nonlinear equation system, time-varying linear equation system, time-varying convex nonlinear optimization under linear equalities, unconstrained time-varying convex nonlinear optimization, time-varying convex quadratic programming under linear equalities, unconstrained time-varying convex quadratic programming, time-varying nonlinear inequality system, time-varying linear inequality system, and time-varying division, are investigated to better understand the essence of zeroing neutral network. Discrete-form time-varying problems are studied by considering the nature of unknown future and the requirement of real-time computation for time-varying problems. A unified model is proposed in the frame of zeroing neural network to uniformly solve these time-varying problems on the basis of their connections and a newly developed discretization formula. Theoretical analyses and numerical experiments, including the tracking control of PUMA560 robot manipulator, verify the effectiveness and precision of the proposed unified model.

In this paper, a new one-step-ahead numerical differentiation rule termed 5-instant discretization formula is proposed for the first-order derivative approximation with higher computational precision. Then, by exploiting the proposed formula to discretize the continuous-time zeroing neural network [or termed, continuous-time Zhang neural network (ZNN)] models, two new discrete-time zeroing neural network [or termed, discrete-time ZNN (DTZNN)] models are proposed, analyzed and investigated for solving systems of discrete time-variant inequalities, including the system of discrete time-variant linear inequalities and the system of discrete time-variant nonlinear inequalities. For comparative purposes, the recently developed Taylor-type DTZNN models and the widely used Euler-type DTZNN models are also presented. Theoretical analyses show that the proposed DTZNN models are convergent, and their steady-state residual errors have an O(g4) pattern with g denoting the sampling gap. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed DTZNN models for solving the systems of discrete time-variant inequalities.

In this paper, a four-point one-step-ahead finite-difference formula is presented, which obtains higher computational precision in approximating the first-order derivative. Then, the formula is used for the discretization of the continuous-time Zhang neural network (CTZNN), and it can greatly overcome the limitation of the conventional formulas in CTZNN discretization. Based on this formula, a new-type discrete-time Zhang neural network (DTZNN) model is proposed and investigated for time-variant matrix pseudoinversion. Numerical experiments further validate the feasibility, effectiveness, and superiority of the proposed new-type DTZNN model for solving the time-variant matrix pseudoinversion. Moreover, the proposed new-type DTZNN model is applied to the control of a robot manipulator. Physical experiment performed on a four-link planar robot manipulator is presented to demonstrate physical realizability and effectiveness of the proposed new-type DTZNN model.