Resilient active seismic response control of structural systems

This paper proposes a dissipative resilient observer and controller (DROC) design for a network controlled system (NCS) that handles faults, implementation errors, or cyberattacks that can be modeled as bounded controller or observer gain perturbations. It presents linear matrix inequality (LMI) conditions for the robust stability of the system in the presence of bounded perturbations in the observer and controller. Furthermore, a new LMI-based time-delay control (TDC) algorithm that mitigates the effects of perturbations due to time-delays in the NCS is introduced. The robust methodology is applied to active control of a scaled model of a structural system equipped with an active mass driver system. The results demonstrate that the proposed methodology is robust and ensures stable system response due to various types of earthquake base excitations.

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

High-Frequency Instabilities of a Boussinesq–Whitham System: A Perturbative Approach

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.

Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

<p style='text-indent:20px;'>In this paper, multidimensional stability of pyramidal traveling fronts are studied to the reaction-diffusion equations with degenerate Fisher-KPP monostable and combustion nonlinearities. By constructing supersolutions and subsolutions coupled with the comparison principle, we firstly prove that under any initial perturbation (possibly large) decaying at space infinity, the three-dimensional pyramidal traveling fronts are asymptotically stable in weighted <inline-formula><tex-math id="M1">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula> spaces on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^{n}\; (n\geq4) $\end{document}</tex-math></inline-formula>. Secondly, we show that under general bounded perturbations (even very small), the pyramidal traveling fronts are not asymptotically stable by constructing a solution which oscillates permanently between two three-dimensional pyramidal traveling fronts on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{4} $\end{document}</tex-math></inline-formula>.</p>

Finite-time synchronization of coupled complex-valued chaotic systems with time-delays and bounded perturbations

In this paper, finite-time synchronization for a class of complex-valued coupled chaotic systems with bounded non-identical perturbations and discontinuous activations is investigated. State feedback controller and Lyapunov function are designed to deal with time delay of the coupled systems. By separating the state variables into real and imaginary parts and using chain rule, sufficient conditions are obtained to realize finite-time synchronization. Moreover, the setting time can be estimated for chaotic systems. Those results can be applied to the continuous and real-valued chaotic systems. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

This paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.