Traffic Matrix (TM), which records traffic volumes among network nodes, is important for network operation and management. Due to cost and operation issues, TMs cannot be directly measured and collected in real time. Therefore, many studies work on predicting future TMs based on historical TMs. However, existing works are usually accuracy-centric prediction solutions that mainly focus on improving predicting accuracy of flows’ sizes (i.e., values of elements in TMs) without considering the practical application of TMs. In this paper, we propose a novel TM prediction solution called Prophet for Traffic Engineering (TE), a typical application for TMs which takes TMs as input to optimize routing. We identify that the critical property (i.e., ) in a TM plays an important role in TE’s performance. Based on this analysis, we adopt the matrix normalization to maintain the critical property in TMs and customize a TE-centric angle loss function to introduce scale invariance of TMs for capturing the overall relationship error. Different from the element-wise Mean Squared Error (MSE) loss function in accuracy-centric prediction solutions, our proposed TE-centric angle loss function has a clear geometric interpretation, which confines the angle between predicted TM and real TM to zero. Simulation results show that the predicted TMs from Prophet can improve the performance of link-level TE and path-level TE by up to 45.4 $\%$ and 52.8 $\%$ , respectively, compared to existing solutions.

The development of machine vision and related technologies in recent years has led to a widespread use of visual servoing in robotics. However, obtaining accurate parameters of camera and robot often necessitates a complex calibration process, making the determination of the projection relationship between image changes and robot joint movements a laborious undertaking. In order to solve the problem, Broyden estimation is applied in this paper to estimate the combined Jacobian matrix online, and the estimation results are then introduced into a model predictive controller to solve the dynamic visual tracking problem, while the constraints of joint angles and velocities are considered. The simulation results verify the effectiveness of the proposed algorithm.

This paper proposes a novel spectral normalized neural networks funnel control approach for servo system with unknown dynamics. The approach introduces spectral normalization technology into the funnel controller design to address the unknown dynamics. Spectral normalization techniques can restrict the spectral norm of the weight matrices of the neural networks, leading to more stable and robust networks. The spectral normalized neural network exhibits strong generalization ability and can adapt to offline learning strategies, which significantly reduce the system's computation cost. Moreover, based on the funnel control architecture, the system output is constrained to remain within an acceptable boundary, optimizing transient performance and guaranteeing satisfactory control performance. All signals of the closed-loop system are bounded based on Lyapunov stability analysis. Finally, simulation results demonstrate that this approach provides commendable tracking performance and superior generalization capabilities.

In recent years, with the development of machine vision and other relative techniques, visual servoing control of robotics has been wildly applied. A complex calibration process is usually required to get the accurate parameters of the camera and the robot, so that getting the projection relationship between changes of images and movement of robot joints usually takes much effort. In order to solve this problem, a rectified linear unit (ReLU) activating neural network (NN) estimator is proposed to estimate the compound Jacobian matrix of the system in this article. The weight of the NN is updated online by a project algorithm with a novel spectral adaptive law which can effectively improve the generalization ability of the NN and the robustness of the system. By constructing a new Lyapunov function with the spectral norm of weight of NN, the stability of the proposed adaptive algorithm and the controller can be proved. Simulations and experimental results validate the effectiveness of the proposed controller.

For a real robot system, it is not easy to use the deep neural networks to approximate the unknown nonlinear dynamics online due to limited computing resources, meanwhile the saturation of the motor also makes it difficult for the system to achieve the desired control effect. In this paper, a method combining spectral normalized deep neural networks and prescribed performance controller with saturated indicator is proposed to solve the problems of insufficient computing resources and input saturation in practical robot system control. Firstly, a low computational cost offline learning spectral normalized deep neural network with rectified linear unit activation is applied in nonlinear dynamics identification to reduce the learning computation burden. The unknown nonlinear dynamics of the robot system including Coriolis force and friction dynamics can be approximated well with good generalization ability by spectral normalized deep neural networks, and the boundedness of the approximation error can be guaranteed by the Lipschitz constraint. Subsequently, a prescribed performance controller with a saturation indicator is also introduced to improve the transient performance of the robot system and eliminate the influence of input saturation. Besides, the closed-loop stability is also proved via the Lyapunov approach. The simulation and experiment results show that the proposed method can achieve good tracking performance and better generalization capability.