Neural networks have shown good results for detecting a certain pattern in a given image. In this paper, faster neural networks for pattern detection are presented. Such processors are designed based on cross correlation in the frequency domain between the input matrix and the input weights of neural networks. This approach is developed to reduce the computation steps required by these faster neural networks for the searching process. The principle of divide and conquer strategy is applied through matrix decomposition. Each matrix is divided into submatrices small in size, and then each one is tested separately by using a single faster neural processor. Furthermore, faster pattern detection is obtained by using parallel processing techniques to test the resulting submatrices at the same time, employing the same number of faster neural networks. In contrast to faster neural networks, the speed-up ratio is increased with the size of the input matrix when using faster neural networks and matrix decomposition. Moreover, the problem of local submatrix normalization in the frequency domain is solved. The effect of matrix normalization on the speed-up ratio of pattern detection is discussed. Simulation results show that local submatrix normalization through weight normalization is faster than submatrix normalization in the spatial domain. The overall speed-up ratio of the detection process is increased as the normalization of weights is done offline.
An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are termed "equivalent subsystems". Local controllers of equivalent subsystems independently tuned for stability and specified feasible performance constitute the decentralized controller guaranteeing specified performance of the full system. To guarantee robust stability, the M−Δ stability conditions are derived. Unlike standard robust approaches, the proposed technique considers full nominal model, thus reducing conservativeness of resulting robust stability conditions. The developed frequency domain design procedure is graphical, interactive and insightful. A case study providing a step-by-step robust DC design for the Quadruple Tank Process [K.H. Johansson: Interaction bounds in multivariable control systems. Automatica 38 (2002), 1045-1051] is included.