Journal of The Franklin Institute-engineering and Applied Mathematics最新文献

In this paper, two kinds of hierarchical time-limited control (HTLC) algorithms with the ability to avoid singularities and simple parameter setting rules are proposed to achieve the bipartite consensus of Networked Lagrange Agents (NLAs), where each agent refers to external disturbances, dynamics uncertainties and bounded inputs. Each HTCL algorithm includes time-limited estimator and prescribed-time local controller. Specially, the HTCL algorithm is developed by combining error transformation and prescribed-time sliding surface. We formally demonstrate that all the states approach the neighborhood of the origin within the prescribed-time, where the settling time can be set only by selecting one parameter. The numerical examples verify the theoretical result.

In this paper, an enhanced parametric detection method employing diversified scan and iteration is proposed for heterogeneous environment. A diversified scan, encompassing both rough scan and intensive scan, is first conducted in the normalized space–time frequency field to acquire the interference’s frequency components, which is conducive to obtaining the outline of interference in the normalized space–time two-dimensional (2-D) frequency field. The intensities of these components are subsequently determined through iteration to reduce the impact brought by the randomness of training samples. Meanwhile, the environment is commonly sparse in most cases, which is fully utilized in the proposed method. Then the cross-correlation matrix and autoregressive (AR) covariance matrix are reconstructed to form the corresponding detector. In the end, the availability and superiority of the proposed method are validated by numerical results. It is shown from numerical results that the proposed method performs well in detection performance compared to several existing typical methods in heterogeneous environment.

This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.

This paper investigates finite-time input-to-state stability (FT-ISS) of impulsive switched systems with multiple impulses. Some FT-ISS conditions, using Lyapunov method and dwell-time condition, are established for impulsive switched systems involving destabilizing and stabilizing impulses simultaneously. When constituent modes regulating continuous dynamics are FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the FT-ISS is retained if impulsive-switching signal satisfies some dwell-time condition. When some constituent modes regulating continuous dynamics are not FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the impulsive-switching signal which satisfies some dwell-time conditions can achieve the FT-ISS of system. In addition, the settling time can be derived conveniently for certain impulsive-switching signal that is formalized by dwell-time condition. The estimation of settling time presents a class of uniformity with respect to the impulsive-switching signals. Two examples are finally presented for the proposed FT-ISS results.

This paper investigates the automatic carrier landing control problem in the presence of model uncertainty, airwake disturbances, input saturation, and output constraints. Considering the performance requirements of the carrier-based aircraft, a composite adaptive neural controller is proposed based on the time-varying barrier Lyapunov function and backstepping control techniques. The radial basis function neural network is used to approximate the model uncertainty, where the neural network weight update law incorporating prediction and tracking errors further improves the convergence rate of the neural network and mitigates high-frequency oscillations. Furthermore, an adaptive disturbance compensation model is established to mitigate the adverse effects of airwake disturbances and estimation errors in the neural network. Based on the Lyapunov stability theory, it is proven that the proposed controller maintains the aircraft trajectory within the prescribed constraints and also ensures that all signals in the closed-loop control system are semiglobally uniformly ultimately bounded. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed composite adaptive neural control method.

Localization technology is crucial for indoor robot navigation. However, because of the intricacies inherent in the indoor setting, the signal transmission is vulnerable to the interference of obstacles, which leads to the decline of positioning accuracy. Ultra-Wideband (UWB) has the characteristics of channel insensitivity and high localization accuracy. Inertial navigation system (INS) functions independently as a navigation system, and its positioning results will not be affected due to non-line-of-sight (NLOS) interference. When using UWB to locate the mobile node, the Variational Bayesian Gaussian Mixture Model (VBGMM) clustering algorithm based on Gaussian Mixture Model (GMM) is applied to lessen the influence of NLOS propagation. This paper proposed a loose coupling of the INS and UWB, which combines the advantages of the two subsystems and improves the performance of the positioning system. On the basis of INS autonomous positioning, the maximum entropy fuzzy generalized probability data association filter (MEF-GPDAF) is used to modify the INS positioning results, and then the virtual inertia points are further built to compensate the error of the corrected coordinates. Finally, Unscented Kalman Filter is applied to the compensated coordinates for enhanced positioning. Simulation indicates that the proposed approach in this paper exhibits superior location accuracy. The real experimental results show that the proposed algorithm achieves an average improvement of 61.12% in positioning accuracy.

Physiological recordings contain a great deal of information about the underlying dynamics of Life. The practical statistical treatment of these single-trial measurements is often hampered by the inadequacy of overly strong assumptions. Heisenberg’s uncertainty principle allows for more parsimony, trading off statistical significance for localization. By decomposing signals into time–frequency atoms and recomposing them into local quadratic estimates, we propose a concise and expressive implementation of these fundamental concepts based on the choice of a geometric paradigm and two physical parameters. Starting from the spectrogram based on two fixed timescales and Gabor’s normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann’s log-normal wavelet. These canonical estimators provide a minimal and flexible framework for single trial time–frequency statistics, which we apply to polysomnographic signals: EEG representations, HRV extraction from ECG, coherence and mutual information between heart rate and respiration.

This paper proposes an observer-based quantized controller for parabolic partial differential equation systems interconnected by a nonlinear coupling protocol. First, a Markov jump model is introduced to describe various randomly occurring actuator failures, and an observer-based pointwise controller is designed under the averaged measurement scheme. Furthermore, taking into account the limitation of network communication resources, a quantization method is adopted to relieve bandwidth pressure. In addition, stability conditions of the closed-loop system with ${\mathscr{H}}_{\infty }$ disturbance attenuation performance are derived by utilizing appropriate Lyapunov functional and inequality techniques. Ultimately, the proposed method is applied to the Fisher equation to verify its feasibility and effectiveness.

This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.