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.

To solve online continuous time-varying convex quadratic-programming problems constrained by a time-varying linear-equality, a novel varying-parameter convergent-differential neural network (termed as VP-CDNN) is proposed and analyzed. Different from fixed-parameter convergent-differential neural network (FP-CDNN) like the gradient-based recurrent neural network, the classic Zhang neural network and the finite-time Zhang neural network (FT-ZNN), VP-CDNN is based on monotonically increasing time-varying design-parameters. Theoretical analysis proves that VP-CDNN has super exponential convergence and the residual errors of VP-CDNN converge to zero even under perturbation situations, which are both better than traditional FP-CDNN and FT-ZNN. Computer simulations based on different activation functions are illustrated to verify the super exponential convergence performance and strong robustness characteristics of the proposed VP-CDNN. A robot tracking example is finally presented to verify the effectiveness and availability of the proposed VP-CDNN.

Two novel nonlinearly activated recurrent neural networks (RNNs) with finite-time convergence [called finite-time RNNs (FTRNNs)] are proposed and analyzed to solve efficiently time-varying systems of nonlinear equations (SoNEs). Compared with previously presented neural networks for solving such a SoNE, the FTRNNs are activated by new nonlinear activation functions and thus possess a better finite-time convergence property. In addition, theoretical analyses about FTRNNs are presented to determine the upper bounds of convergence time under the context of using such two novel nonlinear activation functions. Computer simulations based on a numerical example validate the preponderance of the proposed FTRNNs for time-varying SoNE, as compared to the recently proposed Zhang neural network and its improved version. Finally, an engineering practical example to motion tracking of a robot manipulator demonstrates the feasibility and applicability of the FTRNNs.

Redundancy resolution is of great importance in the control of manipulators. Among the existing results for handling this issue, the quadratic program approaches, which are capable of optimizing performance indices subject to physical constraints, are widely used. However, the existing quadratic program approaches require exactly knowing all the physical parameters of manipulators, the condition of which may not hold in some practical applications. This fact motivates us to consider the application of adaptive control techniques for simultaneous parameter identification and neural control. However, the inherent nonlinearity and nonsmoothness of the neural model prohibits direct applications of adaptive control to this model and there has been no existing result on adaptive control of robotic arms using projection neural network (PNN) approaches with parameter convergence. Different from conventional treatments in joint angle space, we investigate the problem from the joint speed space and decouple the nonlinear part of the Jacobian matrix from the structural parameters that need to be learnt. Based on the new representation, we establish the first adaptive PNN with online learning for the redundancy resolution of manipulators with unknown physical parameters, which tackles the dilemmas in existing methods. The proposed method is capable of simultaneously optimizing performance indices subject to physical constraints and handling parameter uncertainty. Theoretical results are presented to guarantee the performance of the proposed neural network. Besides, simulations based on a PUMA 560 manipulator with unknown physical parameters together with the comparison with an existing PNN substantiate the efficacy and superiority of the proposed neural network, and verify the theoretical results.

Spatial regularization has been proved as an effective method for alleviating the boundary effect and boosting the performance of a discriminative correlation filter (DCF) in aerial visual object tracking. However, existing spatial regularization methods usually treat the regularizer as a supplementary term apart from the main regression and neglect to regularize the filter involved in the correlation operation. To address the aforementioned issue, this article introduces a novel object saliency-aware dual regularized correlation filter, i.e., DRCF. Specifically, the proposed DRCF tracker suggests a dual regularization strategy to directly regularize the filter involved with the correlation operation inside the core of the filter generating ridge regression. This allows the DRCF tracker to suppress the boundary effect and consequently enhance the performance of the tracker. Furthermore, an efficient method based on a saliency detection algorithm is employed to generate the dual regularizers dynamically and provide the regularizers with online adjusting ability. This enables the generated dynamic regularizers to automatically discern the object from the background and actively regularize the filter to accentuate the object during its unpredictable appearance changes. By the merits of the dual regularization strategy and the saliency-aware dynamical regularizers, the proposed DRCF tracker performs favorably in terms of suppressing the boundary effect, penalizing the irrelevant background noise coefficients and boosting the overall performance of the tracker. Exhaustive evaluations on 193 challenging video sequences from multiple well-known challenging aerial object tracking benchmarks validate the accuracy and robustness of the proposed DRCF tracker against 27 other state-of-the-art methods. Meanwhile, the proposed tracker can perform real-time aerial tracking applications on a single CPU with sufficient speed of 38.4 frames/s.

In order to solve the joint-angular-drift problems of redundant robot manipulators, a novel varying-parameter convergent-differential neural network (VP-CDNN) is proposed and exploited. To do so, a quadratic program (QP)-based feedback-considered joint-angulardrift-free (FC-JADF) scheme is first designed and presented. The FC-JADF scheme adopted in this paper is composed of an optimization criterion simultaneously optimizing quadratic and linear terms, and a velocity layer kinematic equation with adding feedback. Second, the FC-JADF scheme is formulated as a standard QP. Third, the VP-CDNN is proposed to solve the resultant standard QP problem. The Lyapunov theory proves that the proposed VP-CDNN solver can globally converge to an optimal solution to the standard QP problem corresponding to redundant robot manipulators, and the joint-angular-drift problems are solved. Two computer simulations and physical experiments based on a six-degree-of-freedom Kinova Jaco² robot, i.e., a starfish path and a cardioid path, verify the effectiveness, accuracy, safety, and practicability of the QP-based FC-JADF scheme and the VP-CDNN solver for solving the joint-angular-drift problems of redundant robot manipulators.