ABSTRACT This article focuses on the time‐varying formation (TVF) control for nonlinear multi‐agent systems (MASs) under dynamic event‐triggered strategies. First, dynamic event triggering (DET) strategies are used to regulate agent‐to‐agent communication and reduce communication costs. Moreover, Zeno behavior is excluded. Second, the neural network (NN)‐based distributed control protocol is designed. The unknown nonlinearities are compensated for using NN approximations. Lyapunov stability analysis shows that the proposed controller guarantees practical TVF tracking. Finally, a numerical example demonstrates the effectiveness of the proposed method.
ABSTRACT Effective frequency‐weighted model order reduction (FWMR) for two‐dimensional (2‐D) discrete‐time systems is essential for high‐speed digital filtering and complex signal processing. However, existing FWMR techniques are fundamentally limited either by the severe computational burden of iterative algorithms and complex Lyapunov inequalities, or by the unacceptably large errors caused by the uneven eigenvalue distribution in current methods. Therefore, this article presents a novel FWMR technique designed for 2‐D decoupled denominator‐type discrete‐time systems to solve these crucial bottlenecks. The core innovation lies in a direct block‐diagonalization strategy applied to the weighted Gramian matrices. Furthermore, the methodology algebraically guarantees the stability of the reduced‐order models under both single‐ and double‐sided frequency weightings. The effectiveness of the proposed approach is comprehensively validated through the performance analysis of three distinct computational 2‐D examples, demonstrating significant improvements over existing state‐of‐the‐art frameworks.
ABSTRACT Due to the presence of flexible components, strong coupling dynamics, underactuation, and non‐minimum‐phase characteristics, achieving simultaneous high‐precision motion tracking and rapid vibration suppression remains a longstanding challenge for flexible manipulators. In this paper, we propose an iterative learning–based nonlinear sliding mode control (IL‐NSMC) scheme for a single‐link flexible manipulator (SLFM). The proposed scheme comprises two synergistic components: (i) a nonlinear sliding mode controller (NSMC) whose sliding surface embeds the rate of flexible vibration energy, in contrast to conventional SMC, whose sliding surface depends solely on the rigid‐joint error and (ii) an iterative learning control (ILC) module that exploits trajectory repetition to compensate for the lumped deviation induced by model uncertainties and external disturbances, requiring no prior knowledge of their bounds and thereby permitting a substantially lower robust gain, which in turn alleviates the chattering that conventional SMC introduces into flexible structures. Convergence in both the time and iteration domains is established via a composite Lyapunov analysis. Comparative simulation studies against conventional sliding mode control (SMC) and multivariable feedback control (MFC) validate the superior effectiveness, feasibility, and practicality of the proposed approach.
This paper investigates the solvability and trajectory controllability of higher-order Hilfer fractional coupled stochastic non-instantaneous impulsive switched differential equations with deviated arguments in the finite-dimensional space. The first part focuses on analyzing the existence of solutions using the M & ouml;nch fixed-point theorem. In the second part, the strongest notion, called trajectory controllability, results are established for the considered system. This study introduces a new class of control functions designed to govern the system at the termination of time intervals and on each impulsive event, incorporating stochastic noise. A numerical example is provided to validate the obtained theoretical results.
In this paper, a new model order reduction approach is presented for reducing large-scale discrete-time singular systems with higher index. Based on the regularity of the singular system, the singular system is decomposed into a non-singular subsystem and a singular subsystem. For the non-singular subsystem, the output matching methods are respectively provided in the time and the frequency domains, so that the outputs of the reduced subsystem match a certain number of the outputs of the original subsystem. For the singular subsystem, output matching methods in both the time and the frequency domains are also obtained. Among them, all the outputs of the reduced non-singular subsystem obtained by the frequency-domain output matching method can theoretically approximate the outputs of the original non-singular subsystem, while the frequency-domain output matching method of the singular subsystem not only enables all outputs to match the original singular subsystem but also ensures the nilpotency of the reduced singular subsystem. Finally, a numerical example is provided to verify the effectiveness of the methods proposed in this paper.
