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In many engineering systems there is a common requirement to isolate the supporting foundation from low frequency periodic machinery vibration sources. In such cases the vibration is mainly transmitted at the fundamental excitation frequency and its multiple harmonics. It is well known that passive approaches have poor performance at low frequencies and for this reason a number of active control technologies have been developed. For discrete frequencies disturbance rejection Harmonic Control (HC) techniques provide excellent performance. In the general case of variable speed engines or motors, the disturbance frequency changes with time, following the rotational speed of the engine or motor. For such applications, an important requirement for the control system is to converge to the optimal solution as rapidly as possible for all variations without altering the system's stability. For a variety of applications this may be difficult to achieve, especially when the disturbance frequency is close to a resonance peak and a small value of convergence gain is usually preferred to ensure closed-loop stability. This can lead to poor vibration isolation performance and long convergence times. In this paper, the performance of two recently developed HC algorithms are compared (in terms of both closed-loop stability and speed of convergence) in a vibration control application and for the case when the disturbance frequency is close to a resonant frequency. In earlier work it has been shown that both frequency domain HC algorithms can be represented by Linear Time Invariant (LTI) feedback compensators each designed to operate at the disturbance frequency. As a result, the convergence and stability analysis can be performed using the LTI representations with any suitable method from the LTI framework. For the example mentioned above, the speed of convergence provided by each algorithm is compared by determining the locations of the dominant closed-loop poles and stability analysis is performed using the open-loop frequency responses and the Nyquist criterion. The theoretical findings are validated through simulations and experimental analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of weakly nonlinear complementarity problems (WNCP) with large sparse matrix. We present an accelerated modulus-based matrix splitting algorithm by reformulating the WNCP as implicit fixed point equations based on two splittings of the system matrixes. We show that, if the system matrix is a P-matrix, then under some mild conditions the sequence generated by the algorithm is convergent to the solution of WNCP. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of efficient iterative algorithms for the large sparse nonsingular saddle point problems based on the upper and lower triangular (ULT) splitting of the coefficient matrix. We call these algorithms ULT methods. First, the ULT algorithm is established and the characteristic of eigenvalues of the iteration matrix of these new methods is analyzed. Then we give the sufficient and necessary conditions for the convergence of these ULT methods. Moreover, the optimal iteration parameters and the corresponding convergence factors for some special cases of the ULT methods are presented. Numerical experiments on a few model problems are presented to support the theoretical results and examine the numerical effectiveness of these new methods. [ABSTRACT FROM AUTHOR]

The present paper deals with the common solution method for finding a fixed point of a nonexpansive mapping and a solution of split hierarchical Minty variational inequality problems. We discuss the weak convergence of the sequences generated by the proposed method to a common solution of a fixed point problem and a split hierarchical Minty variational inequality problem. An example is presented to illustrate the proposed algorithm and result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a split hierarchical monotone variational inclusion problem (SHMVIP) which includes split variational inequality problems, split monotone variational inclusion problems, split hierarchical variational inequality problems, etc., as special cases. An iterative algorithm is proposed to compute the approximate solutions of an SHMVIP. The weak convergence of the sequence generated by the proposed algorithm is studied. We present an example to illustrate our algorithm and convergence result. [ABSTRACT FROM AUTHOR]

In this paper, we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation AXB = C where A and B are symmetric positive definite (SPD). We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual. In particular, the obtained upper bounds for the Gl-FOM method help us to predict the behavior of the Frobenius norm of the Gl-FOM residual. We also explore the worst-case convergence behavior of these methods. Finally, some numerical experiments are given to show the performance of the theoretical results. [ABSTRACT FROM AUTHOR]

A considerable volume of research into adaptive schemes for transmit beamforming in distributed networks has emerged in recent years. A noise-free received signal strength (RSS) measurement and a static environment were often considered. However, in practical scenarios, system uncertainties often arise, which may lead to the aforementioned idealistic assumptions failing. In this paper, we focus on the robust design of distributed beamforming and proposed a systematic analytical framework for the convergence of a general set of adaptive schemes under the condition that the RSS at the receiver is corrupted by noise. Furthermore, we presented theoretical analysis using stochastic stability to demonstrate the tracking capability of the general adaptive schemes when channels are subject to fast time variations. We defined a set of robustness criteria that can be used as comparison metrics for existing adaptive schemes, under time-varying channels and time-varying network topologies. Through the utilization of the proposed analytical frameworks and metrics, we developed a bio-inspired scheme, BioRARSA2, which possess significantly superior robustness with respect to environmental variations and system uncertainties. The improved robustness of the proposed algorithm was validated further through extensive numerical simulations. [ABSTRACT FROM PUBLISHER]