The nonlinear behavior with unpredicted property in engineering has received widespread attention. To explore more unpredicted nonlinear behavior, this paper focuses on the function projective lag synchronization (FPLS) of complex-valued chaotic systems. Most existing control schemes primarily address system stability, lack of consideration in convergence improvement. Zeroing neural dynamics (ZND) has significant results in the convergence performance, yet achieving a balance between model structure and performance remains a challenging task. In light of this, we propose a general time base generator (TBG), and adopt the linear ZND with the simplest structure, which has relatively weak convergence but devoid of nonlinear components, to develop a TBG based neural dynamics controller (TBGBNDC) in the FPLS of complex-valued chaotic systems. The theories illustrate that the system error under the TBGBNDC has predefined-time asymptotic convergence, which is verified in both homogeneous and heterogeneous complex-valued chaotic systems. Compared with other controllers, the TBGBNDC exhibits better performance in terms of convergence, energy and time consumption. Furthermore, the higher-quality random sequences are acquired through the FPLS between these chaotic systems, showing the significant potential application of the research topic.

Given the high coupling of state variables in second-order chaotic systems, the projective synchronization control schemes for first- or fractional-order chaotic systems are not applicable in second-order chaotic systems. Also, the current control schemes on second-order chaotic systems are difficult to tradeoff between convergence and robustness. To address the above issues, this article develops a predefined-time robust neural dynamics controller (PTRNDC). First, a predefined-time nonsingular terminal sliding mode variable (PTNTSMV) is designed to control the coupling of errors in the projective synchronization of second-order chaotic systems, ensuring the nonsingularity and convergence. Hence, a predefined-time double-integral zeroing neural dynamics (ZNDs) design formula based on a time-base generator (TBG) is devised to ensure that the sliding mode variable attains the desired sliding mode surface swiftly and robustly. The theorems about the stability, convergence, and robustness of the projective synchronization under the PTRNDC are analyzed rigorously, and the comparative simulations further verify the effectiveness of the PTRNDC. In addition, the chaotic sequences generated by the projective synchronization between the second-order chaotic systems are successfully applied in the image encryption, making the original image possess excellent visual distortion.

Quadrotor unmanned aerial vehicles (UAVs) have attracted substantial attention due to their simple structure and strong adaptability, but enhancing robustness and adaptability for trajectory tracking under unbounded disturbances remains a key challenge. To address this, this article proposes a novel double integral fuzzy zeroing neural dynamics controller (DIFZNDC). The DIFZNDC integrates a double integral neural dynamics model with a novel dual-input single-output fuzzy logic system (DISOFLS), which can adaptively adjust the parameters, thereby enhancing the robustness and adaptability of the controller. In addition, the global convergence and robustness of the system under the DIFZNDC are theoretically verified. Moreover, two trajectory tracking examples demonstrate the effectiveness and superiority of the DIFZNDC for the quadrotor system. Quantitative analysis under Gaussian disturbance indicates that the DIFZNDC reduces the root-mean-square error (RMSE) by 84.61% and 48.35% compared to the modified super-twisting controller (MSTC) and the fixed-time zeroing neural dynamics controller (FTZNDC), respectively.

With the advancement of robotic-assisted minimally invasive surgery, visual servo control has become a crucial technique for improving surgical outcomes. However, traditional visual servo methods often rely on precise kinematic models and camera calibration, limiting their generalizability. Considering these, this article proposes a novel uncalibrated model-free visual servo control scheme. Specifically, we introduce a Jacobian matrix and interaction matrix estimation method based on a gradient neural network (GNN), which enables online estimation by utilizing control signals and sensor outputs. Then, the estimated results are incorporated into a visual servo control framework that considers remote center of motion (RCM) constraint, joint-drift problem, and physical constraint, formulated as a quadratic programming (QP) problem. Subsequently, focusing on the joint limits and endoscope insertion depth constraint, we develop a nonpiecewise differentiable multilevel constraint handling technique. For the formulated QP problem, a predefined-time convergent error-regulating zeroing neural network (PTCER-ZNN) solver is designed, and we can derive the optimal control signals. Detailed theoretical analyses of the developed GNN estimation method and the PTCER-ZNN solver are provided. Simulation results demonstrate the effectiveness of the proposed scheme in image feature regulation and tracking tasks, exhibiting its advantages over existing approaches.

The permanent magnet synchronous generator (PMSG) system becomes unstable when unpredicted chaos appears, and current approaches do not take how to lessen this chaos phenomenon into account. Motivated by the ability of projective synchronization (PS) to adjust the chaotic system trajectory, this research aims to use PS to reduce the chaos in PMSG system. For better control in the time estimation of PS and the robustness of systems, an adaptive predefined-time robust zeroing neural dynamic controller (APTRZNDC) for the PS between PMSG systems is proposed. In the process, an adaptive parameter determined by the system error is designed with the demand for higher convergence factor in the case of large error. In addition, a nonlinear activation function contributed to the predefined-time synchronization is created, making the upper bound of synchronization time independent of system initial states and parameters, except for a single predefined parameter. Moreover, essential theorems for the predefined-time PS and robustness under the APTRZNDC are supplied and validated. And better robustness of PMSG system with the APTRZNDC is demonstrated when compared with other controllers. Furthermore, the APTRZNDC is applied in secure communication via the PS of PMSG systems, which guarantees both the timeliness of signals and the immunity of communication.

In real-world scenarios, quadrotors face significant noise challenges from both internal and external sources, necessitating more robust controllers. While most existing models assume bounded noise, unbounded noise poses greater practical challenges. To address this, we propose a novel controller design method based on variant-parameter double integral multi-layer neural dynamics (VP-DIMND) for quadrotors. First, the design process of the quadrotor’s position and attitude controller based on the VP-DIMND method is presented. Second, theoretical analysis demonstrates that the VP-DIMND controller ensures rapid convergence and robust performance against various noise conditions, including bounded and unbounded noises. This is achieved through the use of variant-parameter multi-layer zeroing neural dynamics and double integral design mode. Finally, simulation experiments show that the VP-DIMND controller effectively enables the quadrotor track the given time-varying tasks in various noisy environments. Moreover, compared with similar methods, the proposed VP-DIMND method improves the convergence speed by about 40%, and the tracking results under the VP-DIMND controller outperforms the existing controllers, including convergence and robustness. These results also highlight the potential of the VP-DIMND controller for enhancing the stability and reliability of quadrotor in noisy environments.

Involving both position and orientation tracking, pose tracking control for the end-effector of a redundant manipulator is a critical problem in robotic motion control. However, existing methods often suffer from dependency on model parameters and lack joint constraints. To remedy these weaknesses, this article proposes a data-based predictive tracking control of position and orientation (DBPTCPO) for redundant manipulators with undetermined parameters. Specifically, in addition to minimizing tracking error, the DBPTCPO scheme can also minimize joint velocity and acceleration to optimize energy efficiency. Furthermore, it directly handles three-level joint constraints, effectively preventing a reduction in the feasible domain of decision variables. As for the uncertain parameters of redundant manipulators, a method based on zeroing neurodynamics (ZNs) is developed to estimate the Jacobian matrix, requiring only the sensory output and control signals. Ultimately, a ZN-based solver is designed to solve the quadratic programming (QP) problem with inequality constraints derived from the DBPTCPO scheme. Necessary theoretical analyses for the control process are provided, and the higher tracking accuracy of the proposed method is numerically validated when compared with other control schemes.

Time-varying linear equations (TVLEs) play a fundamental role in the engineering field and are of great practical value. Existing methods for the TVLE still have issues with long computation time and insufficient noise resistance. Zeroing neural network (ZNN) with parallel distribution and interference tolerance traits can mitigate these deficiencies and thus are good candidates for the TVLE. Therefore, a new predefined-time adaptive ZNN (PTAZNN) model is proposed for addressing the TVLE in this article. Unlike previous ZNN models with time-varying parameters, the PTAZNN model adopts a novel error-based adaptive parameter, which makes the convergence process more rapid and avoids unnecessary waste of computational resources caused by large parameters. Moreover, the stability, convergence, and robustness of the PTAZNN model are rigorously analyzed. Two numerical examples reflect that the PTAZNN model possesses shorter convergence time and better robustness compared with several variable-parameter ZNN models. In addition, the PTAZNN model is applied to solve the inverse kinematic solution of UR5 robot on the simulation platform CoppeliaSim, and the results further indicate the feasibility of this model intuitively.

Solving nonlinear equation flows is the one critical step in statistics and control fields. Access to its real-time solutions has become a major challenge for scholars. Numerous research work has confirmed the effectiveness of zeroing neural dynamics (ZND) for time-varying problems. Accordingly, this paper constructs a novel predefined-time neural dynamics (NPTND) model for nonlinear equation flows. To address exponential convergence of the linear ZND model, the time-base generator is utilized in the design formula of NPTND model, giving the model predefined-time approximate convergence. Whereafter, numerical comparative simulations in two different dimensions are performed to assess the effectiveness of the NPTND model. Specifically, the NPTND model has predefined-time approximate convergence and a certain robustness against small noise in solving process.

Zeroing neural network (ZNN) can effectively solve the matrix flows inversion problem. Nevertheless, quite a few related research works focus on the improvement of the convergence and robustness performance of the ZNN models and ignore the conservatism of their predefined time. Therefore, this article adopts a polymorphous activation function (PAF) to construct a new predefined time ZNN (NPTZNN) model. The second method of Lyapunov is utilized to analyze the stability, convergence, and robustness of the NPTZNN model. The Beta function is dexterously employed in the process of calculating the predefined time of the NPTZNN model, reducing its conservatism. Furthermore, the correctness of the theoretical analyses is verified by numerous experiments. Finally, the NPTZNN model is applied to robot manipulator control and can improve the tracking speed, extending the applicability of the model.

In this article, a novel adaptive robust predefined-time nonsingular sliding mode control (ARPTNSMC) scheme is investigated, which aims to achieve fast and accurate tracking control of a quadrotor subjected to external disturbance. Inspiration is drawn from a fuzzy neural network that is constructed by fuzzy logic and zeroing neural network (ZNN). Distinct from most sliding mode control approaches, two nonsingular sliding mode surfaces are formulated by employing general ZNN approaches and differentiable predefined-time activation functions. Furthermore, for the compensation of external disturbance, a dynamic adaptive parameter and a fuzzy adaptive parameter are designed in the attitude control law. The fuzzy adaptive parameter, generated by the Takagi–Sugeno fuzzy logic system, is incorporated to enhance the robustness while reducing the chattering phenomena resulting from the discontinuous sign function. Theoretical proofs are provided to demonstrate the predefined-time convergence and robustness of the closed-loop system. Finally, two trajectory tracking examples are offered to validate the convergence, robustness, and low-chattering characteristics of the closed-loop system under the developed ARPTNSMC scheme.

With high wind speed, low turbulence, and high output, offshore wind power has gradually become a new area of wind power development. Nevertheless, the chaos phenomenon of offshore wind turbines manifests in some severe environments and the entire power generation system is affected. A variety of projective synchronization schemes are proposed to control this phenomenon, but the research on fixed-time projective synchronization of offshore wind turbine systems (OWTSs) is scant and has flaws in robustness. Motivated by zeroing neural dynamics (ZND) with fixed-time convergence, this article presents a fixed-time robust controller (FXTRC) based on ZND for the projective synchronization of OWTSs. In design process, a novel activation function is constructed to guarantee the projective synchronization speed and enhance the robustness. It is rigorously calculated that the upper bound of the projective synchronization time is only related to system parameters. Furthermore, the projective synchronization progress of OWTSs under the FXTRC displays better robustness compared with other controllers, which is proven by simulation results.