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The method of orthogonal projection is introduced according to the problem of feed forward parameter optimization in linear servo system with high frequency response. At first, orthogonalized basis functions are constructed and the control system is projected onto the axes of the basis functions. Then system parameters are identified along the axes of basis functions by iterative learning and high...
This paper aims at the H∞ fixed-interval smoothing problem for linear continuous-time systems with l + 1 time-delay observations. Such problem will be converted into H2 fixed-interval smoothing problem for linear time-delay systems in indefinite space. Therefore, the H∞ fixed-interval smoothing problem is solved by using the orthogonal projection theory in indefinite space, and the fixed-interval...
In this paper, we discuss the moment problem of g-frames in Hilbert spaces. Firstly, we give the definition of moment problem which is based on operators, and discuss the necessary and sufficient conditions of the existence of its solution. Secondly, we discuss its best approximative solution by orthogonal projection when it has no exact solution.
The generalized Laguerre-generalized Hermite mixed spectral method is developed. Various orthogonal projections are investigated. Some mixed approximation results are established. As an example of their important applications, a mixed spectral scheme is proposed for two-dimensional non-isotropic heat conduction equation. Its convergence is proved. Numerical results demonstrate the high accuracy of...
The projections and projection matrices are widely used (see e.g., Basilevsky 1983; Gray bill 1983; Horn and Johnson 1990; Lütkepohl 1996). The projections and projection matrices with respect to the symmetric positive and nonnegative definite matrices are often used in algebra and statistics (see e.g., Rao and Mitra 1971; Searle1982; Harville, 1997; Abadir and Magnus 2005). Recently, Wang (2010)...
A complex domain projection method of analysis is proposed based on the transient representation of electro-magnetic traveling wave (EM) for transmission line. Considering the impact of distributed parameters and the characteristics of electro-magnetic wave, the transmission line model is built. The instantaneous voltage equation and the fault location function are derived and obtained and the former...
This paper deals with subspace-based identification of unstable systems. Because the system is unstable, we will assume the experimental data are generated under stabilizing feedback. In order to remove the effect of noise an orthogonal projection is used. The system state space matrices are recovered from the extended observability matrix. The subspace-based identification algorithm is tested on...
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