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This paper focuses on iterative parameter estimation methods for a nonlinear closed-loop system (i.e., a nonlinear feedback system) with an equation-error model for the open-loop part. By applying negative gradient search, a gradient-based iterative algorithm is constructed. To reduce the computational costs and improve the parameter estimation accuracy, the hierarchical identification principle is employed to derive a hierarchical gradient-based iterative algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.

The autoparametric vibration absorber is a device that reduces the resonance amplitude in a main system using nonlinear interactions. In this study, we consider a cantilever-type autoparametric vibration absorber and propose two methods to enhance performance via linear and nonlinear feedback control. To decrease the response amplitude at the anti-resonance point, we compensate for the viscous damping of the absorber by actuating the supporting point of the cantilever according to the feedback control with respect to the absorber velocity. In the state where the energy is transferred from the main system into the absorber, the absorber amplitude becomes large. Then, because the natural frequency is shifted from the linear natural frequency owing to the nonlinear stiffness of the absorber, the frequency ratio between the absorber and the main system deviates from a suitable ratio such as 1:2. To avoid this shift, we eliminate the cubic nonlinear stiffness of the absorber via cubic nonlinear feedback control with respect to the displacement of the absorber. By performing nonlinear analysis of the governing equations of the main system and the absorber under the control methods, we examine the absorber performance depending on the linear and nonlinear feedback gains. Furthermore, we conduct experiments using a simple apparatus. The results demonstrate the validity of the proposed control methods.

In this paper, we propose a design approach of composite nonlinear feedback control technique for the synchronization of master/slave nonlinear systems with time-varying delays, Lipschitz nonlinear functions and parametric uncertainties. Based on the Lyapunov–Krasovskii stabilization theory and linear matrix inequalities, a new sufficient condition is generated for the synchronization of chaotic systems with nonlinearities and perturbations on the master and slave systems. By using the Barbalat’s lemma, the proposed control method guarantees that the states of the master and slave systems are synchronized with an asymptotic convergence rate. Simulation results are demonstrated on two forms of Chua’s chaotic system, which illustrate that the suggested design technique yields satisfactory transient performance.

Chaos may arise in many nonlinear evolution equations which make the dynamics much more complex. In this study, we report the finding of a novel chaotic attractor in a modified KdV–Burgers–Kuramoto (mKBK) equation. For potential applications, we further study analytically its chaos synchronization including complete synchronization with known and unknown parameters, generalized functional projective synchronization (GFPS) with known and unknown parameters, and combined synchronization with known and unknown parameters via the designed nonlinear feedback controllers. Numerical illustrations are presented which agree well with the theoretical results.

The digital images are widely captured, transmitted, and stored by limited resource devices. Those devices need lightweight encryption (LWE) techniques to protect secret and personal images. Designing LWE algorithms for digital images is challenging due to the large size and high inter-pixel correlations of digital images. This paper presents an image encryption technique based on the Nonlinear feedback shift register (NLFSR) and DNA computation. The image is permuted first using pseudorandom sequence generated by a NLSFR based Key stream generator followed by a substitution of pixel values using DNA computations in cipher block chaining mode. Furthermore, security analysis tests, histograms, correlation, entropy, NPCR, and UACI are used to verify our scheme. The security and performance analysis of the proposed techniques analyses showed their efficacy and resistance to attacks. The analysis of the results certainly indicates the scheme is highly secure and lightweight. The proposed scheme can be used for secure image transmission and storage in medical IoT, smart surveillance, etc.

This paper presents an approach of achieving high performance and robustness for matched uncertain multi-input multi-output linear systems with external disturbances and multiple state-delays, which are often encountered in practice and are frequently the sources of instability. This scheme is based on composite nonlinear feedback and integral sliding mode control methods. The selection of nonlinear function and the existence of sliding mode are two important issues, which have been addressed. The control law is designed to guarantee the existence of the sliding mode around the nonlinear surface, and the damping ratio of the closed-loop system is increased as the output approaches the set-point. Simulation results are presented to show the effectiveness of the proposed method as a promising way for controlling similar nonlinear systems.

In this paper, the load frequency control (LFC) for networked microgrids in the presence of delayed electric vehicles (EVs) aggregator and renewable energy sources (RESs) like photovoltaic, wind turbine and fuel cell have been investigated. A linear active disturbance rejection control (LADRC) technique based on the extended state observer (ESO) and nonlinear feedback control law (NLFCL) is proposed to eliminate the frequency variations resulted from the load disturbance and uncertainty of RESs. Since the LADRC parameters could be designed by the ESO and controller bandwidths, the presented controller could have similar performance with the fixed-structured controller. Also, the IMC technique is used for the robust tuning of the LADRC controller. The simulation is carried out on the three-area LFC scheme containing EVs aggregator, RESs, and fuel cell. According to simulation results, the LADRC controller has fewer frequency variations in contrast to other methods presented in the case studies.

This study presents an experimental method for identification of the backbone curves of cantilevers using the nonlinear dynamics of a van der Pol oscillator. The backbone curve characterizes the nonlinear stiffness and nonlinear inertia of the resonator, so it is important to identify this curve experimentally to realize high-sensitivity and high-accuracy sensing resonators. Unlike the conventional method based on the frequency response under external excitation, the proposed method based on self-excited oscillation enables direct backbone curve identification, because the effect of the viscous environment is eliminated under the linear velocity feedback condition. In this research, the method proposed for discrete systems is extended to give an identification method for continuum systems such as cantilever beams. The actuation is given with respect to both the linear and nonlinear feedbacks so that the system behaves as a van der Pol oscillator with a stable steady-state amplitude. By varying the nonlinear feedback gain, we can produce the self-excited oscillation experimentally with various steady-state amplitudes. Then, using the relationship between these steady-state amplitudes and the corresponding experimentally measured response frequencies, we can detect the backbone curve while varying the nonlinear feedback gain. The efficiency of the proposed method is determined by identifying the backbone curves of a macrocantilever with a tip mass and a macrocantilever subjected to atomic forces, which are representative sources of hardening and softening cubic nonlinearities, respectively.

Nonlinear feedback shift registers (NFSRs) are used in many recent stream ciphers as their main building blocks. One security criterion for the design of a stream cipher is to assure its used NFSR has a long period. As the period of a Fibonacci NFSR is equal to its largest cycle length, a common way to get a maximum-period Fibonacci NFSR is to join the cycles of an original Fibonacci NFSR into a maximum cycle. Nevertheless, so far only the maximum-period Fibonacci NFSRs with stage numbers no greater than 33 have been found. Considering that Galois NFSRs may have higher implementation efficiency than Fibonacci NFSRs, this paper first generalizes the cycle joining method for Fibonacci NFSRs to Galois NFSRs and establishes some conditions for maximum-period Galois NFSRs. It then reveals the cycle structure of some cascade connections of two Fibonacci NFSRs. Based on both, the paper constructs some long-period Galois NFSRs including maximum-period Galois NFSRs with stage numbers up to 41. Finally, it analyzes their hardware implementation via the technology mapping obtained by synthesizing the NFSRs with Synopsys Design Compiler L - 2016.03-Sp1 using the TSMC 90nm CMOS library, and the results show that they have good hardware performance.

Considering the security of a communication system, designing a high-dimensional complex chaotic system suitable for chaotic synchronization has become a key problem in chaotic secure communication. In this paper, a new 5-D hyperchaotic system with high order nonlinear terms was constructed and proved to be hyperchaotic by dynamical characterization characteristics, the maximum Lyapunov exponent was close to 2, and there was a better permutation entropy index, while a valid chaotic sequence could be generated in three cycles in the FPGA (Field Programmable Gate Array)-based implementation. A multivariable nonlinear feedback synchronous controller based on FPGA was proposed to design and implement synchronization of high order complex hyperchaotic systems. The results show that the error signal converged to 0 rapidly under the effect of the nonlinear feedback synchronous controller. This lays the foundation for the synchronization of high order complex chaotic systems.