Global exponential stability of uncertain neural networks with discontinuous Lurie-type activation and mixed delays

Fixed-Time Stabilization of Discontinuous Neutral Neural Networks With Proportional Delays via New Fixed-Time Stability Lemmas

When studying the stability of time-delayed discontinuous systems, Lyapunov-Krasovskii functional (LKF) is an essential tool. More relaxed conditions imposed on the LKF are preferred and can take more advantages in real applications. In this article, novel conditions imposed on the LKF are first given which are different from the previous ones. New fixed-time (FXT) stability lemmas are established using some inequality techniques which can greatly extend the pioneers. The new estimations of the settling times (STs) are also obtained. For the purpose of examining the applicability of the new FXT stability lemmas, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is formulated which is more generalized than the existing ones. Using differential inclusions theory, set-valued map, and the newly obtained FXT stability lemma, some algebraic FXT stabilization criteria are derived. Finally, examples are given to show the correctness of the established results.

Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-Order Derivatives

Tracking control for multiple-integrator systems is regarded as a fundamental problem associated with nonlinear dynamic systems in the physical and mathematical sciences, with many applications in engineering fields. In this paper, we adopt the Zhang neural network method to solve this nonlinear dynamic problem. In addition, in order to adapt to the requirements of real-world hardware implementations with higher-order precision for this problem, the multiple-order derivatives in the Zhang neural network method are estimated using backward finite-divided difference formulas with quadratic-order precision, thus producing time delays. As such, we name the proposed method the Zhang neural network method with time delay. Moreover, we present five theorems to describe the convergence property of the Zhang neural network method without time delay and the quadratic-order error pattern of the Zhang neural network method with time delay derived from the backward finite-divided difference formulas with quadratic-order precision, which specifically demonstrate the effect of the time delay. Finally, tracking controllers with quadratic-order precision for multiple-integrator systems are constructed using the Zhang neural network method with time delay, and two numerical experiments are presented to substantiate the theoretical results for the Zhang neural network methods with and without time delay.

A Novel Supertwisting Zeroing Neural Network With Application to Mobile Robot Manipulators

Various zeroing neural network (ZNN) models have been investigated to address the tracking control of robot manipulators for the capacity of parallel processing and nonlinearity handling. However, two limitations occur in the existing ZNN models. The first one is the convergence time that tends to be infinitely large. The second one is the research of robustness that remains in the analyses of stability and asymptotic convergence. To simultaneously enhance the convergence performance and robustness, this article proposes a new ZNN model by using a supertwisting (ST) algorithm, termed STZNN model, for the tracking control of mobile robot manipulators. The proposed STZNN model inherently possesses the advantages of finite-time convergence and robustness making the control process fast and robust. The bridge from the sliding mode control to the ZNN is built, and the essential connection between the ST algorithm and ZNN is explored by constructing a unified design process. Theorems and proofs about global stability, finite-time convergence, and robustness are provided. Finally, path-tracking applications, comparisons, and tests substantiate the effectiveness and superiority of the STZNN model for the tracking control handling of mobile robot manipulators.