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A hierarchical sliding mode control approach is proposed for a class of SIMO under-actuated systems. This class of under-actuated systems is made up of several subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows. At first, the sliding surface of every subsystem is defined. Then the sliding surface of one subsystem is defined as the first layer sliding surface. The first layer sliding surface is used to construct the second layer sliding surface with the sliding surface of another subsystem. This process continues till the sliding surfaces of the entire subsystems are included. According to the hierarchical structure, the total control law is deduced by the Lyapunov theorem. In theory, the asymptotic stability of the entire system of sliding surfaces is proven and the parameter boundaries of the subsystem sliding surfaces are given. Simulation results show the feasibility of this control method through two typical SIMO underactuated systems. [ABSTRACT FROM AUTHOR]

In many pattern recognition tasks (e.g., handwritten letters), it is essential to recognize a given pattern invariantly with translation, rotation, and other spatial transformations to which the pattern might be subjected. The Fourier transform method is a well-known method for translation invariant pattern recognition in which the Fourier spectrum of an image is used as an invariant feature. This paper shows experimentally that a three-layer neural network learns to have a similar capability to that of the Fourier transform method by means of the back propagation learning, during which a set of random dot patterns are repeatedly presented with various positions. Specifically, each unit in the middle layer of the resultant network detects a particular frequency component contained in the given image; and, using the information, the output layer generates an output pattern which is invariant to translation of the image. [ABSTRACT FROM AUTHOR]