A ROBUST PHASE-ONLY DIRECT DATA DOMAIN ALGORITHM BASED ON GENERALIZED RAYLEIGH QUOTIENT OPTIMIZATION USING HYBRID GENETIC ALGORITHM

A robust phase-only Direct Data Domain Least Squares (D3LS) algorithm based on gen- eralized Rayleigh quotient optimization using hybrid Genetic Algorithm (GA) is presented in this letter. The optimization efficiency and computational speed are improved via the hybrid GA com- posed of standard GA and Nelder-Mead simplex algorithms. First, the objective function, with a form of generalized Rayleigh quotient, is derived via the standard D3LS algorithm. It is then taken as a fitness function and the unknown phases of all adaptive weights are taken as decision variables. Then, the nonlinear optimization is performed via the hybrid GA to obtain the optimized solution of phase-only adaptive weights. As a phase-only adaptive algorithm, the proposed algorithm is sim- pler than conventional algorithms when it comes to hardware implementation. Moreover, it proc- esses only a single snapshot data as opposed to forming sample covariance matrix and operating matrix inversion. Simulation results show that the proposed algorithm has a good signal recovery and interferences nulling performance, which are superior to that of the phase-only D3LS algorithm based on standard GA.

Generalized Rayleigh quotient and finite element two-grid discretization schemes

This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.

Novel passive localization algorithm based on weighted restricted total least square

A novel multi-observer passive localization algorithm based on the weighted restricted total least square （WRTLS） is proposed to solve the bearings-only localization problem in the presence of observer position errors. Firstly, the unknown matrix perturbation information is utilized to form the WRTLS problem. Then, the corresponding constrained optimization problem is transformed into an unconstrained one, which is a generalized Rayleigh quotient minimization problem. Thus, the solution can be got through the generalized eigenvalue decomposition and requires no initial state guess process. Simulation results indicate that the proposed algorithm can approach the Cramer-Rao lower bound （CRLB）, and the localization solution is asymptotically unbiased.

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (II)

When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick_Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).