A Jump-Gain Integral Recurrent Neural Network for Solving Noise-Disturbed Time-Variant Nonlinear Inequality Problems.

Nonlinear inequalities are widely used in science and engineering areas, attracting the attention of many researchers. In this article, a novel jump-gain integral recurrent (JGIR) neural network is proposed to solve noise-disturbed time-variant nonlinear inequality problems. To do so, an integral error function is first designed. Then, a neural dynamic method is adopted and the corresponding dynamic differential equation is obtained. Third, a jump gain is exploited and applied to the dynamic differential equation. Fourth, the derivatives of errors are substituted into the jump-gain dynamic differential equation, and the corresponding JGIR neural network is set up. Global convergence and robustness theorems are proposed and proved theoretically. Computer simulations verify that the proposed JGIR neural network can solve noise-disturbed time-variant nonlinear inequality problems effectively. Compared with some advanced methods, such as modified zeroing neural network (ZNN), noise-tolerant ZNN, and varying-parameter convergent-differential neural network, the proposed JGIR method has smaller computational errors, faster convergence speed, and no overshoot when disturbance exists. In addition, physical experiments on manipulator control have verified the effectiveness and superiority of the proposed JGIR neural network.

Design, Analysis, and Application of a Discrete Error Redefinition Neural Network for Time-Varying Quadratic Programming.

Time-varying quadratic programming (TV-QP) is widely used in artificial intelligence, robotics, and many other fields. To solve this important problem, a novel discrete error redefinition neural network (D-ERNN) is proposed. By redefining the error monitoring function and discretization, the proposed neural network is superior to some traditional neural networks in terms of convergence speed, robustness, and overshoot. Compared with the continuous ERNN, the proposed discrete neural network is more suitable for computer implementation. Unlike continuous neural networks, this article also analyzes and proves how to select the parameters and step size of the proposed neural networks to ensure the reliability of the network. Moreover, how to achieve the discretization of the ERNN is presented and discussed. The convergence of the proposed neural network without disturbance is proven, and bounded time-varying disturbances can be resisted in theory. Furthermore, the comparison results with other related neural networks show that the proposed D-ERNN has a faster convergence speed, better antidisturbance ability, and lower overshoot.

A Punishment Mechanism-Combined Recurrent Neural Network to Solve Motion-Planning Problem of Redundant Robot Manipulators.

In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

Mutual-Collision-Avoidance Scheme Synthesized by Neural Networks for Dual Redundant Robot Manipulators Executing Cooperative Tasks.

Collision between dual robot manipulators during working process will lead to task failure and even robot damage. To avoid mutual collision of dual robot manipulators while doing collaboration tasks, a novel recurrent neural network (RNN)-based mutual-collision-avoidance (MCA) scheme for solving the motion planning problem of dual manipulators is proposed and exploited. Because of the high accuracy and low computation complexity, the linear variational inequality-based primal-dual neural network is used to solve the proposed scheme. The proposed scheme is applied to the collaboration trajectory tracking and cup-stacking tasks, and shows its effectiveness for avoiding collision between the dual robot manipulators. Through network iteration and online learning, the dual robot manipulators will learn the ability of MCA. Moreover, a line-segment-based distance measure algorithm is proposed to calculate the minimum distance between the dual manipulators. If the computed minimum distance is less than the first safe-related distance threshold, a speed brake operation is executed and guarantees that the robot cannot exceed the second safe-related distance threshold. Furthermore, the proposed MCA strategy is formulated as a standard quadratic programming problem, which is further solved by an RNN. Computer simulations and a real dual robot experiment further verify the effectiveness, accuracy, and physical realizability of the RNN-based MCA scheme when manipulators cooperatively execute the end-effector tasks.

Design and Analysis of a Novel Integral Recurrent Neural Network for Solving Time-Varying Sylvester Equation.

To solve a general time-varying Sylvester equation, a novel integral recurrent neural network (IRNN) is designed and analyzed. This kind of recurrent neural networks is based on an error-integral design equation and does not need training in advance. The IRNN can achieve global convergence performance and strong robustness if odd-monotonically increasing activation functions [i.e., the linear, bipolar-sigmoid, power, or sigmoid-power activation functions (SP-AFs)] are applied. Specifically, if linear or bipolar-sigmoid activation functions are applied, the IRNN possess exponential convergence performance. The IRNN has finite-time convergence property by using power activation function. To obtain faster convergence performance and finite-time convergence property, an SP-AF is designed. Furthermore, by using the discretization method, the discrete IRNN model and its convergence analysis are also presented. Practical application to robot manipulator and computer simulation results with using different activation functions and design parameters have verified the effectiveness, stability, and reliability of the proposed IRNN.

Convergence and Robustness Analysis of Novel Adaptive Multilayer Neural Dynamics-Based Controllers of Multirotor UAVs.

Because of the simple structure and strong flexibility, multirotor unmanned aerial vehicles (UAVs) have attracted considerable attention among scientific researches and engineering fields during the past decades. In this paper, a novel adaptive multilayer neural dynamic (AMND)-based controllers design method is proposed for designing the attitude angle (the roll angle ϕ , the pitch angle θ , and the yaw angle ψ ), height ( z ), and position ( x and y ) controllers of a general multirotor UAV model. Global convergence and strong robustness of the proposed AMND-based method and controllers are analyzed and proved theoretically. By incorporating the adaptive control method into the general multilayer neural dynamic-based controllers design method, multirotor UAVs with unknown disturbances can complete time-varying trajectory tracking tasks. AMND-based controllers with the self-tuning rates can estimate the unknown disturbances and solve the model uncertainty problems. Both the theoretical theorems and simulation results illustrate that the proposed design method and its controllers with strong anti-interference property can achieve the time-varying trajectory tracking control stably, reliably, and effectively. Moreover, a practical experiment by using a mini multirotor UAV illustrates the practicability of the AMND-based method.

A Penalty Strategy Combined Varying-Parameter Recurrent Neural Network for Solving Time-Varying Multi-Type Constrained Quadratic Programming Problems.

To obtain the optimal solution to the time-varying quadratic programming (TVQP) problem with equality and multitype inequality constraints, a penalty strategy combined varying-parameter recurrent neural network (PS-VP-RNN) for solving TVQP problems is proposed and analyzed. By using a novel penalty function designed in this article, the inequality constraint of the TVQP can be transformed into a penalty term that is added into the objective function of TVQP problems. Then, based on the design method of VP-RNN, a PS-VP-RNN is designed and analyzed for solving the TVQP with penalty term. One of the greatest advantages of PS-VP-RNN is that it cannot only solve the TVQP with equality constraints but can also solve the TVQP with inequality and bounded constraints. The global convergence theorem of PS-VP-RNN is presented and proved. Finally, three numerical simulation experiments with different forms of inequality and bounded constraints verify the effectiveness and accuracy of PS-VP-RNN in solving the TVQP problems.

An Exponential-Type Anti-Noise Varying-Gain Network for Solving Disturbed Time-Varying Inversion Systems.

To solve the disturbed time-varying inversion problem, an exponential-type anti-noise varying-gain network (EAVGN) is proposed and analyzed. To do so, a vector-based error function is first defined. By using the varying-gain neural dynamic design method, an EAVGN model is then formulated. Furthermore, the differentiation error and the model-implementation error are considered into the model, and the perturbed EAVGN model is obtained. For better illustrations, comparisons between the EAVGN and the conventional fixed-parameter recurrent neural network (FP-RNN) are conducted to illustrate the advantages of the proposed EAVGN. Mathematical proof demonstrates that the proposed EAVGN has much better anti-noise properties than FP-RNN. On one hand, the residual error of EAVGN can be reduced to zero in any case, but that of FP-RNN is large and cannot be convergent, in particular when the bound of Frobenius norm of the exact solution is large or the noise is large. On the other hand, the bound of the residual error of EAVGN is always smaller than that of FP-RNN. Simulation results verify that when different types of noises exist, the proposed EAVGN owns better anti-noise property compared with the state-of-the-art methods. In addition, a practical application is presented to illustrate the implementation process and the practical benefits of the EAVGN.

Power-Type Varying-Parameter RNN for Solving TVQP Problems: Design, Analysis, and Applications.

Many practical problems can be solved by being formulated as time-varying quadratic programing (TVQP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (VPNN) is proposed and analyzed to effectively solve the resulting TVQP problems, as well as the original practical problems. For a clear understanding, we introduce this model from three aspects: design, analysis, and applications. Specifically, the reason why and the method we use to design this neural network model for solving online TVQP problems subject to time-varying linear equality/inequality are described in detail. The theoretical analysis confirms that when activated by six commonly used activation functions, VPNN achieves a superexponential convergence rate. In contrast to the traditional zeroing neural network with fixed design parameters, the proposed VPNN has better convergence performance. Comparative simulations with state-of-the-art methods confirm the advantages of VPNN. Furthermore, the application of VPNN to a robot motion planning problem verifies the feasibility, applicability, and efficiency of the proposed method.

A Complex Varying-Parameter Convergent-Differential Neural-Network for Solving Online Time-Varying Complex Sylvester Equation.

A novel recurrent neural network, which is named as complex varying-parameter convergent-differential neural network (CVP-CDNN), is proposed in this paper for solving the time-varying complex Sylvester equation. Two kinds of CVP-CDNNs (i.e., CVP-CDNN Type I and Type II) are illustrated and proved to be effective. The proposed CVP-CDNNs can achieve super-exponential performance if the linear activation function is used. Some activation functions are considered for searching the better performance of the CVP-CDNN and the finite time convergence property of the CVP-CDNN with sign-bi-power activation function is testified. The convergence time of the CVP-CDNN with sign-bi-power activation function is shorter than complex fixed-parameter convergent-differential neural network (CFP-CDNN). Moreover, compared with traditional CFP-CDNN, better convergence performances of novel CVP-CDNN are verified by computer simulation comparisons.

A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation.

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.