Robust decentralized adaptive output feedback fuzzy controller design and application to AHS

A novel decentralized indirect adaptive output feedback fuzzy controller is developed for a class of large-scale uncertain nonlinear systems using error filtering.By the properly filtering of the observation error dynamics,the strictly positive-real condition is guaranteed to hold such that the proposed output feedback and adaptation mechanisms are practicable in practice owing to the fact that its implementation does not require the observation error vector itself any more,which corrects the impracticable schemes in the previous literature involved.The presented control algorithm can ensure that all the signals of the closed-loop large-scale system keep uniformly ultimately bounded and that the tracking error converges to zero asymptotically.The decentralized output feedback fuzzy controller can be applied to address the longitudinal control problem of a string of vehicles within an automated highway system（AHS） and the effectiveness of the design procedure is supported by simulation results.

Reference satellite selection method for GNSS high-precision relative positioning

Selecting the optimal reference satellite is an important component of high-precision relat/ve positioning because the reference satellite directly influences the strength of the normal equation. The reference satellite selection methods based on elevation and positional dilution of precision （PDOP） value were compared. Results show that all the above methods cannot select the optimal reference satellite. We introduce condition number of the design matrix in the reference satellite selection method to improve structure of the normal equation, because condition number can indicate the ill condition of the normal equation. The experimental results show that the new method can improve positioning accuracy and reliability in precise relative positioning.

On Conditionally Positive Definite Dot Product Kernels

Let m and n be fixed, positive integers and P a space composed of real polynomials in m variables. The authors study functions f ： R →R which map Gram matrices, based upon n points of R^m, into matrices, which are nonnegative definite with respect to P Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functions

Observer-based Variable Universe Adaptive Fuzzy Controller Without Additional Dynamic Order

A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.

A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem

The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.