Invariance Principles and Observability in Switched Systems with an Application in Consensus

Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak observability (WO) associated with this output. WO is what the output informs about the limiting behavior of state trajectories (hidden in the zero locus of the output). In the context of switched NLTV systems, WO can be explored using the recently established framework of limiting zeroing-output solutions. Adding to this, an extension of the integral invariance principle for switched NLTV systems with a new method to guarantee uniform global attractivity of a closed set (without assuming uniform Lyapunov stability or dwell-time conditions) is proposed. By way of illustrating the proposed method, a leaderless consensus problem for nonholonomic mobile robots with a switching communication topology is addressed, yielding a new control strategy and a new convergence result

A Modification of Minimal Residual Iterative Method to Solve Linear Systems

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear system Ax=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR

A Novel Near-Real-Time GB-InSAR Slope Deformation Monitoring Method

In the past two decades, ground-based synthetic aperture radars (GB-SARs) have developed rapidly, providing a large amount of SAR data in minutes or even seconds. However, the real-time processing of big data is a challenge for the existing GB-SAR interferometry (GB-InSAR) technology. In this paper, we propose a near-real-time GB-InSAR method for monitoring slope surface deformation. The proposed method uses short baseline SAR data to generate interferograms to improve temporal coherence and reduce atmospheric interference. Then, based on the wrapped phase of each interferogram, a network method is used to estimate and remove systematic errors (such as atmospheric delay, radar center shift error, etc.). After the phase unwrapping, a least squares estimator is used for the overall solution to obtain the initial deformation parameters. When new data are added, a sequential estimator is used to combine the previous processing results and dynamically update the deformation parameters. Sequential estimators could avoid repeated calculations and improve data processing efficiency. Finally, the method is validated with the measured data. The results show that the average deviation between the proposed method and the overall estimation was less than 0.01 mm, which could be considered a consistent estimation accuracy. In addition, the calculation time of the sequential estimator was less sensitive than the total amount of data, and the time-consuming growth rate of each additional period of data was about 1/10 of the overall calculation. In summary, the new method could quickly and effectively obtain high-precision surface deformation information and meet the needs of near-real-time slope deformation monitoring