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

Most of the previous image encryption schemes overlook certifying the source of the encrypted images, thus the receiver may be misled by messages coming from unauthorized users or wrong sources. To simultaneously accomplish image encryption and source authentication of the encrypted images, an optical image authentication and encryption scheme is proposed by integrating computational ghost imaging (CGI) with quick response (QR) code. Firstly, the plaintext image is converted into a QR code and encrypted by a scrambling-diffusion structure. Then, the authentication image is enciphered by a CGI system and a diffusion structure. The intermediate resulting images are marked and embedded into the random matrices to withstand the differential attack. Moreover, the source of the encrypted images can be identified by the reconstructed authentication image and the nonlinear correlation coefficient (NCC) result. The authentication is considered successful if a sharp peak appears in the center of the NCC result. Numerical simulations show that the proposed scheme can not only withstand different attacks, but also avoid being misled by misinformation during the decryption process.

This paper mainly studies the exponential synchronization issue of chaotic neural networks with parametric uncertainties and time-varying delays via hybrid impulsive control and delay compensatory strategy. Considering the hybrid impulses and flexible delays in the controller, the idea of average delayed impulsive gain (ADIG) is introduced to quantify the effects of hybrid impulses from a comprehensive viewpoint, i.e., not only the desynchronizing/synchronizing delay-free impulses but also the desynchronizing/synchronizing delayed impulses are discussed. Meanwhile, the impulsive delays are fetched and integrated to compensate the desynchronizing impulses dynamically, which removes certain strict restrictions on the impulsive gains and impulsive delays compared with existed works. Correspondingly, some relaxed sufficient criteria for exponential synchronization are derived by jointly utilizing the concept of average delayed impulsive gain, the delay compensatory scheme and the mathematical induction methodology. Ultimately, two examples with some comparisons are given to verify the applicability and superior performance of the obtained results.

This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.

This study introduces an advanced methodology for estimating the source term of multiple, variable-number biochemical hazard releases, where the exact count of sources is not predetermined. Focusing on environments monitored via a network of sensors, we tackle this challenge through a multi-source Bayesian filtering paradigm, employing the theory of random finite sets (RFS). Our novel approach leverages a modified particle filter-based probability hypothesis density (PHD) filter within the RFS framework, enabling simultaneous estimation of critical source characteristics (such as location, emission rate, and effective release height) and the quantification of source numbers. This method not only accurately estimates pertinent source parameters but is also adept at identifying the emergence of new sources and the cessation of existing ones within the monitored area. The efficacy of our approach is validated through extensive simulations, which mimic a range of scenarios with varying and unknown source counts, highlighting the proposed method’s robustness and precision.

This paper investigates the leader-following mean square distributed tracking control problem (DTCP) for a Markov jump multiagent systems (MJMASs) with the general linear dynamical model over an undirected graph. The non-strict control input of the leader is non-zero, unknown, and unavailable to any followers. First, the jump characteristics of the system for the single agent is modeled by a continuous Markov chain. Second, in order to address the leader–follower mean square DTCP, the distributed mode-dependent static controller and the fully distributed mode-dependent adaptive controller are designed for all followers based on the information from the agents’ neighbors and itself, respectively. Then, to further analyze the stability of the MJMASs, two categories of decomposed related Lyapunov functions are constructed using Lyapunov stability theory. The sufficient conditions for the existence of the distributed controller are obtained by derivation. Finally, two simulation cases are presented to verify the validity and feasibility of the proposed strategies.

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and $S$-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

This paper presents a robust $H_{\infty }$ stabilization approach for actively controlled systems that include uncertain input time-delay. The approach comprises two essential steps: (1) converting a controlled system with uncertain time-delay to have only deterministic time-delay through a time-scale transformation; and (2) applying the Chebyshev spectral continuous time approximation (CHsCTA) method and defining appropriate extension matrices to transform the system so there are no time-delays. A robust $H_{\infty }$ control design is implemented on the transformed system, which facilitates the derivation of a robust $H_{\infty }$ controller. An iterative algorithm is proposed for computing the feedback gain matrix, which overcomes the challenges posed by the nonlinear coupling terms when solving the matrix inequalities. Case studies validate the effectiveness of the proposed control algorithm, which, through comparison with existing control algorithms, is shown to be less conservative.

Oxygen starvation may occur when oxygen is not replenished quickly after a sudden increase of load in fuel-cell-powered vehicles, leading to permanent damage to the fuel cell membrane. To avoid this phenomenon, the oxygen excess ratio (OER) is usually estimated through observers as it cannot be measured directly. Since observers may suffer from model mismatches that lead to inaccurate OER estimation, a possible modification to the fuel cell system is proposed in this work by including an oxygen flow sensor at its exhaust. Yet the response of this sensor is slow, and to compensate for the slow response of the sensor, a novel two-degree-of-freedom PI controller and a state observer are designed to provide a robust, accurate, and quick estimation and control of the OER.

This paper studies the trajectory tracking problems of unmanned ground vehicle with model uncertainties and external disturbances. We propose a finite-time control method, in which the uncertainty and disturbance compensating is considered. To match the real motion scenarios of vehicles, the Frenet-coordinate system is used and the error dynamics equation is constructed. A new type of coordinate transformation is adopted to simplify the calculation of finite-time stability. Further, we design a new finite-time disturbance observer to deal with the model uncertainties and external disturbances. Based on this observer, the finite-time trajectory tracking controller is constructed by using a new integral-type Lyapunov function. It is theoretically proved that all tracking errors in the closed-loop system are finite-time stable. To verify the feasibility, simulation on the unmanned ground vehicle has been conducted.

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.